Complex Numbers and Quadratic Equations — practice questions

230 curated practice questions from Complex Numbers and Quadratic Equations (Mathematics JEE Main, NTA Exams) — 159 easy, 40 medium, 31 hard. Every question includes the final answer free; step-by-step worked solutions with a free account.

• If z is any complex number such that z+ 1 z =1, then the value of z^ 99 + 1 z^ 99 is
• The general value of θ which satisfies the equation ( +i )( 3 +i 3 ) [ (2 n-1) +i (2 n-1) ]=1 (where r = 0, 1, 2, 3…
• The number of complex numbers z such that | z – 1| = | z + 1 | = | z – i | equals
• If the roots of the equation (x - b) (x - c) + (x - c) (x - a) + (x -a) (x - b) = 0 are equal, then
• If l , m, n are real, l ≠ m, then the roots of the equation ( l – m) x 2 – 5 ( l + m) x – 2 ( l – m) = 0 are
• If 5 z_ 2 7 z_ 1 is purely imaginary number, then find the value of | 2 z_ 1 +3 z_ 2 2 z_ 1 -3 z_ 2 |
• The value of (1- + ^ 2 )^ 5 + (1+ - ^ 2 )^ 5 , where and ^ 2 are the complex cube roots of unity, is
• The amplitude of sin 5 +i (1- 5 ) is
• The integral value of x satisfing |x 2 + 4x + 3| + 2x + 5 = 0 is
• If a,b,c are distinct rational numbers then roots of equation (b+c-2 a) x^ 2 +(c+a-2 b) x+(a+b-2 c)=0 are
• The number of non-zero integral solutions of the equation |1-i|^ x = z ^ x is
• If ω (≠ 1) is a cube root of unity and (1 + ω) 7 = A + Bω. Then, A + 2B (where A, B ∈ R ), equals to
• The roots of the equation x^ 2 +p x+q=0 are tan 22º and tan 23º then
• The value of amp (iω) + amp (iω 2 ), where i= -1 and = [3] 1 = non-real, is
• The harmonic mean of the roots of the equation (5+ 2 ) x^ 2 -(4+ 5 ) x+(8+2 5 )=0
• i^ 2 +i^ 4 +i^ 6 + upto (2 k+1) terms, k N is
• If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 50, then |z| is
• Let z= +i -i , 4 < < 2 . Then, arg (z) is
• If |z_ 1 |=1, |z_ 2 |=2, |z_ 3 |=3 and |9 z_ 1 z_ 2 +4 z_ 3 z_ 1 +z_ 2 z_ 3 |=6, then value of |z_ 1 +z_ 2 +z_ 3 | is
• For any two complex numbers z 1 and z 2 and any two real numbers a and b, |a z_ 1 -b z_ 2 |^ 2 + |b z_ 1 +a z_ 2 |^ 2…
• If the roots of the equation x^ 2 -b x+c=0 be two consecutive integers, then b^ 2 -4 c equals
• The equation (x - a) 3 + (x - b) 3 + (x - c) 3 = 0 has
• Find the common roots of equation z^ 3 +2 z^ 2 +2 z+1=0 and 2^ 1185 +2^ 100 +1=0 .
• If is an imaginary cube root of unity, then (1+ - ^ 2 )^ 2 equals
• If |z 1 | = |z 2 | = ... = |z n | = 1, then the value of |z 1 + z 2 + z 3 + ... + z n | is:
• If a _ 1 are the roots of the equation ax 2 + bx + c = 0, then a +b + a +b is equal to
• If the inequality (m-2) x^ 2 +8 x+m+4>0 is satisfied for all x R then the least integral m is:
• The product of the real roots of the equation |2x + 3| 2 – 3 |2x + 3| + 2 = 0, is
• If complex number z = x + iy satisfies the equation Re (z + 1) = |z - 1|, then z lies on
• If 1, _ 1 ^ 2 are cube roots of unity, then (1+ ) (1+ ^ 2 ) (1+ ^ 4 ) (1+ ^ 6 ) is equal to
• If x + iy = (1 + i) (1 + 2i) (1 + 3i), then x 2 + y 2 =
• The smallest positive integer n for which (1+i)^ 2 n =(1-i)^ 2 n is
• Given below are two statements. STATEMENT - 1 (Assertion): If 5 z_ 2 11 z_ 1 is purely imaginary then, | 2 z_ 1 +3 z_ 2…
• The sum of the roots of the equation, x 2 + |2x - 3| - 4 = 0, is 2 k . Then value of k is
• If both the roots of the quadratic equation x 2 – 2kx + k 2 + k – 5 = 0 are less than 5, then k lies in the interval
• In a quadratic equation with leading coefficient 1, a student reads the coefficient 16 of x wrongly as 19 and obtain…
• If |z- 4 z |=z then the maximum value of |z| is equal to
• The value of _ k=1 ^ 10 ( 2 k 11 +i 2 k 11 ) i 5
• If for real a, b, c, d,(a+i b)^ [+i d is real, then it is equal to :
• The equation Im ( i z-2 z-i )+1=0, z G, z i . represents a part of a circle having radius equal to:
• Let x = -1+i 3 2 if a=(1+a) _ k=a ^ 1010 a^ 2 k and b= _ k=m ^ 10 m ^ 3 k then a and b are the roots of the quadratic…
• If the roots of the quadratic equations x 2 + px + q = 0 are tan 30 o and tan 15 o respectively, then the value of 2 +…
• The roots of the equation |x 2 – x – 6| = x + 2 are
• For any complex number z, the minimum value of |z|+|z-1| is :
• If II and are the roots of the equation x 2 - p(x + 1) - q = 0, then the value of a^ 2 +2 a+1 a^ 2 +2 a+q + ^ 2 +2 +1 ^…
• If the product of the roots of the equation x ^ 2 - 3 k x + 2 e ^ 2 lng k -1= 0 is 7. Then the roots of the equation…
• Let p, q R. If 2- 3 is a root of the quadratic equation, x^ 2 +p x+q=0 , then:
• The value of | a | , where II is a non-real cube root of unity is
• If a,b,c R, the equation and x^ 2 +2 x+3=0 have a common root, then a : b : c =
• If α and β are the roots of x^ 2 -P(x+1)-C=0, then the value of ^ 2 +2 +1 ^ 2 +2 +C + ^ 2 +2 +1 ^ 2 +2 +C is
• If P, Q, R, S are represented by the complex numbers 4 + i, 1 + 6i, - 4 + 3i, - 1 - 2i respectively, then PQRS is a
• If z 1 , z 2 are any two complex numbers, then :
• If is complex cube root of unity and a, b, c are three real numbers such that array l 1 a+ + 1 b+ + 1 c+ =2 ^ 2 and 1…
• If z is a non-zero complex number, then | z |^ 2 z z is equal to
• A value of b for which the equations array l x^ 2 +b x-1=0 x^ 2 +x+b=0 array have one root in common is
• The inequality |z-4|<|z-2| represents the region given by
• array l If z_ r = ( 3^ r )+i ( 3^ r ), r=1,2,3 Then value of z_ 1 z_ 2 z_ 3 . . is array
• The roots of the quadratic equation 7x 2 – 9x + 2 = 0 are
• Product of real roots of the equation x ^ 2 +| x |+ 9 = 0
• If the equations x^ 2 +p x+q=0 and x^ 2 +q x+p=0 have a common root then (p+q+1) is equal to
• The modulus and amplitude of (1+i 3 )(2+2 i) ( 3 -i) are respectively
• If 3 p^ 2 =5 p+2 and 3 q^ 2 =5 q+2 where p ≠ q, then the equation whose roots are 3 p-2 q and 3 q-2 p is
• Let II and be the roots of x^ 2 -6 x-2=0 , with x> . If a_ n =x^ n - ^ n for n ≥ 1, then the value of a_ 1! -2 a_ ! 2…
• Given below are two statements. STATEMENT - 1: Let z be a complex number, then the equation z^ 4 +z+z=0 cannot have a…
• The real value of a for which the quadratic equation 2 x^ 2 - [a^ 3 +8 a-1 ] x+a^ 2 -4 a=0 possesses roots of opposite…
• If p, q, r are positive numbers and are in A.P., then the roots of quadratic equation p x 2 + q x + r = 0 are real for
• If 1, II 1 , .......... II n - 1 are the n th roots of unity and n is an odd natural number then (1 + II 1 )(1 + II 2…
• For a < 0 determine all real roots of equation x^ 2 -2 a|x-a|-3 a^ 2 =0 .
• The least positive integer n such that ( 2 i 1+ i )^ n is a positive integer, is
• The sum of 10 th power of 4 th roots of unity is
• If ω (≠ 1) is a complex cube root of unity, the least value of n ∈ N for which (1+ ^ 2 )^ 7 = (1+ ^ 4 )^ 7 is
• The number of integral solutions of x+1 x^ 2 +2 > 1 4 is :
• If ( 1) is a cube root of unity and (1+ )^ 7 =A+B , then A and B are respectively
• The value of a for which one root of the quadratic equation (a 2 – 5a + 3) x 2 + (3a – 1) x + 2 = 0 is twice as large…
• If II , β are roots of equation 8 x^ 2 -3 x+27=0 then the value of [ ( z ^ 2 / ]^ 1 / 3 + [ ^ 2 / z ]^ 1 / 3 ] i 5:
• If 3+2 i 1-2 i is purely imaginary then θ is
• If z_ 1 and z_ 2 are complex numbers satisfying both the equations |z|= 5 and | z- 2 (1+i) z |=1 then find |z_ 1 -z_ 2…
• The value of sum _ n=1 ^ 13 (i^ n +i^ n+1 ) where equals
• The value of
• Let z be a complex number such that | z-1 z+2 i |=1 and |z|= 5 2 . Then the value of | z + 3 i| is :
• The real part of 1 1- +i is equal to
• If the equation (k – 2) x 2 – (k – 4) x – 2 = 0 has difference of roots as 3 then the value of k is
• The number of real values of m for which the equation x^ 3 -m x^ 2 +3 x-2=0 has two roots equal in magnitude but…
• The value of k for which the equation 3x 2 + 2x (k 2 + 1) + k 2 – 3k + 2 = 0 has roots of opposite signs, lies in the…
• If II and β ( II < β) are the roots of the equation x 2 + bx + c = 0 when c < 0 < b, then
• If the equation x^ 2 +b x+45=0(b R) has conjugate complex roots and they satisfy |z+1|=2 10 , then:
• If ( 1+i 1-i )^ x =1 , then the value of integer x is
• If a, b, c are in GP, then the equations a x^ 2 +2 b x+c=0 and d x^ 2 +2 e x+f=0 have a common root, if d a , e b , f c…
• If α, β are the roots of the equation x 2 – p (x + 1) –c =0, then (α + 1) (β + 1) =
• If unity is double repeated root of p x^ 3 +q (x^ 2 +x )+r=0 , then
• The distance of the roots of the equation _ n z^ n + _ 1 z^ n-1 + + _ n =3 from origin, where _ n , _ 1 , _ 2 , , _ n…
• If e i θ = cos θ + i sin θ, then for the ∆ABC, e iA . e iB . e iC is
• If (1 – p) is a root of quadratic equation x 2 + px + (1 – p) = 0, then its roots are
• If P represents the variable complex number z and Re ( z+1 z+i )=1 , then the locus of P is
• If II , β, γ, σ are the roots of the equation x 4 + 4x 3 - 6x 2 + 7x - 9 = 0, then the value of (1 + II 2 ) (1 + β 2 )…
• If the cube roots of unity are 1, ω, ω 2 , then the roots of the equation (x – 1) 3 + 8 = 0, are:
• If x+ 1 x =2 x_ 1 then x^ n + 1 x^ n is equal to
• If z 1 = 2 ( 4 +i 4 ) and z 2 = 3 ( 3 +i 3 ) then |z 1 z 2 | is
• Let i= -1 . If (-1+i 3 )^ 21 (1-i)^ 24 + (1+i 3 )^ 21 (1+i)^ 24 =k, and n=[|k|] be the greatest integral part of Then _…
• If equations ax 2 + bx + c = 0, (a, b R, a 0) and 2x 2 + 3x + 4 = 0 have a common root then a : b : c equals:
• If α and β be the roots of the equation x^ 2 -7 x+2=0 , then the least value of n for which ( x )^ n =1 is:
• Find the value of p if 3x 2 - 2x + p = 0 and 6x 2 - 17x + 12 = 0 have a common root
• The value of a so that the equations (2 a-5) x^ 2 -4 x-15=0 and (3 a-8) x^ 2 -5 x-21=0 have a common root, is
• If z = x – iy and z 1/3 = p + iq, (where x,y,p,q ∈ R ) then ( x p + y q ) ( p ^ 2 + q ^ 2 ) equal to
• The complex numbers z 1 , z 2 and z 3 satisfying z_ 1 -z_ 3 z_ 2 -z_ 3 = 1-i 3 2 are the vertices of a triangle which is
• The number of real roots of the equation, e^ 4 x +e^ 3 x -4 e^ 2 x +e^ x +1=0
• Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always
• If x+i y = (a+i b) , then -x-i y is equal to
• If x, , Y are the roots of the equation a x^ 3 +b x^ 2 +c=0 , then the equation whose roots are x + , + x , x + is :
• The number of roots of the equation 3 x^ _ 5 2 +2^ _ 5 x =64 is
• The integer value of ‘ k ’ such that x^ 2 -2(4 k-1) x+15 k^ 2 -2 k-7>0 x R is
• If n is a positive integer, then (1+i)^ n +(1-i)^ -n is equal to :
• If p and q are the roots of the equation x^ 2 +p x+q=0 , then
• If the sum of the squares of the roots of the equation x^ 2 -( x-2) x-(1+ x)=0 is least, then II is
• A possible value of is
• Let II and be two fixed non zero complex numbers and z be a variable complex number. If the lines x z + x z+1=0 and z +…
• If a,b,c are distinct rational numbers and a + b + c = 0, then the roots of the equation (b+c-a) x^ 2 +(c+a-b)…
• If roots of the quadratic equation a 1 x 2 + b 1 x + c 1 = 0 are II 1 , 1 and those of a 2 x 2 + b 2 x + c 2 = 0 are II…
• If one root of quadratic equation ax 2 + bx + c = 0 is equal to nth power of the root, then value of (a c^ n )^ 1 n+1 +…
• If two equations a_ 1 x^ 2 +b_ 1 x+c_ 1 =0 and a_ 2 x^ 2 +b_ 2 x+c_ 2 =0 have a common root, then the value of (a_ 1 b_…
• If roots of the equation x 2 + ax + 25 = 0 are in the ratio of 2 : 3 then the value of a is
• The value of is equal to
• If , are roots of the equation a x^ 2 +3 x+2=0(a<0), then ^ 2 + ^ 2 is greater than
• The value of _ k =1 ^ 6 ( 2 k 7 -i 2 k 7 ) is k i , then value of k is
• Let II , II 2 be the roots of x^ 2 +x+1=0 , then the equation whose roots are II 31 , II 62 is
• If a, b, c are distinct positive real numbers and a 2 + b 2 + c 2 = 1, then ab + bc + ac is
• If the roots of the equations x 2 + 3x + 2 = 0 & x 2 – x + λ = 0 are in the same ratio of 4 9 then the value of λ is…
• The number of integral value of m for which the equation (1+m^ 2 ) x^ 2 -2(1+3 m) x+8 m=0 has no real roots is
• If a+i b = x + iy, then possible value of a-i b is
• Let z - i be any complex number such that z-i z+i is a purely imaginary number then z+ 1 z is:
• Let z, w be complex numbers such that z +i w =0 and arg (zw) = π. Then, arg (z) equals
• If (x + iy) = 1+2 i 3+4 i , then (x 2 + y 2 ) 2 is equal to
• If x = a + b, y = aα + bβ, z = aβ + bα, where α, β are complex cube roots of unity, (a, b ∈ R ), then xyz equals
• The equation b z+b z =c where b is a non zero complex constant and c is real, represents
• Let (-2- i 3 )^ 3 = x+i y 27 ,(i= -1 ) , where x and y are real numbers, then y - x equals:
• If z 1 and z 2 are two non-zero complex numbers such that |z 1 + z 2 | = |z 1 | + |z 2 |, and arg z 1 – arg z 2 is…
• If the number (z-1) (z+1) is purely imaginary, then |z|=
• The number of the real solutions of the equation 2|x|^ 2 -5|x|+2=0 is
• The equation e sin x –e – sin x – 4 = 0 has how many real roots
• Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT …
• If α and β are roots of the equation, x 2 –4 kx + 2e 4 ln k - 1 = 0 for some k, and then is equal to . Find the value…
• If ω is a cube root of unity, then (3 + 5ω + 3ω 2 ) 2 + (3 + 3ω + 5ω 2 ) 2 is equal to
• Find the value of _ r=1 ^ 5 [ ( 2 r 7 )- icos ( 2 r 7 ) ]
• If the equation (a^ 2 +4 a+3 ) x^ 2 + (a^ 2 -a-2 ) x+a(a+1)=0 has more than two roots, then value of a is
• How many real solutions does the equation x^ 7 +14 x^ 5 +16 x^ 3 +30 x-560=0 have ?
• If the difference between the roots of the equation x 2 + ax + 1 = 0 is less than 5 , then the set of possible values…
• The complex numbers z = x + iy which satisfy the equation | z-5 i z+5 i |=1, lie on
• If ( 1+ i 1- i )^ x =1, then
• Product of real roots of the equation x 2 + |x| + 9 = 0
• If and are the roots of x ^ 2 + x +1=0 , then ( ^ 15 + ^ 15 ) is equal to
• Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and…
• If x_ 1 be the roots of x^ 2 +p x+q=0 and y, be the roots of x^ 2 +p x+r=0 then ( - )( - ) ( - )( - ) =
• If arg (z) = θ, then arg ( Z ) is equal to
• All the values of m for which both roots of the equation x 2 – 2mx + m 2 –1 = 0 are greater than –2 but less than 4…
• If 2= 7-i 3-4 i then z^ 14 is equal to
• Suppose z 1 , z 2 , z 3 are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z 1 = 1 + i 3 …
• If z 1 , z 2 , z 3 are complex numbers such that |z 1 | = |z 2 | = |z 3 | = | 1 z_ 1 + 1 z_ 2 + 1 z_ 3 |=1, then |z 1 +…
• P represents the variable complex number z and | 2z - 3 | = 2, then the locus of P is
• If z = x + iy and w = (1 - iz) / (z - i), then |w| = 1 implies that, in the complex plane
• If a _ 1 be the two roots of the equation x 2 + x + 1 = 0, then the equation whose roots are x and x is :
• If z and ω are two non-zero complex numbers such that |zω| = 1 and Arg (z) - Arg(ω) = 2 , then 2 is equal to
• The value of 'a' for which one root of quadratic equation (a^ 2 -5 a+3 ) x^ 2 +(3 a-1) x+2=0 is twice as large as the…
• If z is a complex number such that |z| ≥ 2, then the minimum value of |z+ 1 2 | is K, then find 10K.
• If x 2 - x + 1 = 0, then the value of _ n=1 ^ 5 (x^ n + 1 x^ n )^ 2 is
• If (2+ 3 )^ x^ 2 -2 x+1 +(2- 3 )^ x^ 2 -2 x-1 = 2 2- 3 and x > 0 then, the value of x is
• Let II and be the roots of the equation x ^ 2 + x +1=0 . The equation whose roots are x^ 19 , ^ 7 is
• If Re ( z-1 2 z+i )=1 , where z = x + iy, then the point (x, y) lies on a:
• If α, β are roots of Ax 2 + Bx + C = 0 and α 2 , β 2 are roots of x 2 + px + q = 0, then p is equal to
• The number of real roots of the equation (x-1)^ 2 +(x-2)^ 2 +(x-3)^ 2 =0 is
• The number of all possible positive integral values of α for the roots of the quadratic equation, 6 x^ 2 -11 x+ a = 0…
• Let p(x) be a quadratic polynomial such that p(0) = 1, if p(x) leaves remainder 4 when divided by x - 1 and it leaves…
• The sum of all real roots of the equation |x – 2| 2 + |x – 2| – 2 = 0, is
• Let A= E (- 2 , ): 3+2 i 1-2 i is purely imaginary . Then the sum of the elements in A is:
• If p, q are the roots of the equation x^ 2 +p x+q=0 where both p and q are non-zero, then (p, q) =
• If a _ 1 are roots of equation p (x^ 2 +n^ 2 )+p n x+q n^ 2 x^ 2 =0 then p (x^ 2 + ^ 2 )+p x +q x^ 2 ^ 2 =
• The equation z z +(2-3 i) z+(2+3 i) z +4=0 represents a circle of radius
• If z is a complex number, then z^ 2 + z ^ 2 =z represents
• If 7 and r are the roots of the equation p x^ 2 +q x+r=0 , then
• If w= z z- 1 3 i and |w|=1 , then z lies on
• If a ∈ R and the equation –3 (x – [x]) 2 + 2 (x – [x]) + a 2 = 0 (where [x] denotes the greatest integer ≤ x) has no…
• For positive integers n 1 , n 2 the value of expression (1+ i )^ n _ 1 + (1+ i ^ 3 )^ n _ 1 + (1+ i ^ 5 )^ n _ 2 + (1+…
• The value of a for which the sum of the squares of the roots of the equation x^ 2 -(a-2) x-a-1=0 assume the least value…
• If a 2 + b 2 = 1, then 1+ b + ia 1+ b - ia is equal to :
• The value of 1 + i 2 + i 4 + i 6 + ... + i 2n is :
• C is the complex numbers f: C R is defined by f(z)= |z^ 3 -z+z | . The maximum value of f on the circle |z|=1 is
• If then x is equal to
• The number of solutions for the equation x^ 2 -5|x|+6=0 is/are:
• If the difference between the roots of x 2 + ax + b = 0 and x 2 + bx + a = 0 is same and a ≠ b, then
• Find all the values of c for which complex number z satisfy the equation |z|^ 2 -2 i z+2 c(1+i)=0 .
• If ω is a non-real cube root of unity, then the expression (1–ω) (1–ω 2 ) (1+ω 4 ) (1+ω 8 ) is equal to
• Let II and be the roots of equation p x^ 2 +q x+r=0, p 0 . If p, q, r are in A.P. and 1 x + 1 =4 , then the value of |…
• For any two complex numbers z 1 and z 2 and any real numbers a and b; |(az 1 – bz 2 )| 2 + |(bz 1 + az 2 )| 2 is equal…
• If A, G and H are respectively AM, GM and HM of three positive numbers a, b and c, then equation whose roots are a, b…
• Let a _ 1 be real and z be a complex number, z^ 2 + z+ =0 has two distinct roots on the line Re z = 1, then it is…
• If is non real cube root of unity then, the value of (1+ - ^ 2 )^ 2 + (1- + ^ 2 )^ 2 is equal to :
• The points z 1 , z 2 , z 3 , z 4 in the complex plane are the vertices of a parallelogram taken in order, if and only if
• If _ k=0 i^ k =x+i y , then the value of x =
• For all complex numbers z of the form 1 + i , R , if z 2 = x + iy, then value of y 2 + 4x is
• If z is a complex number of unit modulus and argument θ, then arg ( 1+z 1+ z ) equals:
• If ω is an imaginary cube root of unity, then (1 + w – w 2 ) 7 is equal to
• If then 4+5 (- 1 2 + i 3 2 )^ 334 -3 ( 1 2 + i 3 2 )^ 365 is equal to
• For real parameter t, the locus of the complex number z= (1-t^ 2 )+i 1+t^ 2 in the complex plane is
• If a and b ( ≠ 0) are the roots of equation x 2 + a x + b = 0, then least value of x 2 + a x + b is
• The range of values of m for which the equation (m-5) x^ 2 +2(m-10) x+m+10=0 has real roots of the same sign, is given…
• If a _ 1 be the roots of x ^ 2 - a ( x -1)+ b = 0 , then the value of 1 a^ 2 -a a^ 2 + 1 ^ 2 -a + 2 a+b is
• If a _ 1 & , are the roots of x 2 - px + q = 0 and x 2 - γx + s = 0 respectively, then find the value of ( -Y)( - )+(…
• If square root of –7 + 24i is x + iy. If x = ± k, then value of k is
• Area of Δ whose vertices are points z 1 , z 2 , z 3 on the argand diagram, is
• If z 1 , z 2 and z 3 , z 4 are 2 pairs of complex conjugate numbers, and arg ( z_ 1 z_ 4 )+ ( z_ 2 z_ 3 ) equals kπ…
• The perpendicular distance of line (1-i) z+(1+i) z +3=0 , from (3+2 i) will be
• If x, , Y are the roots of the equation x ^ 3 + x +1=0 , then the value of x^ 3 + ^ 3 +y^ 3 is
• If z= ( 3 2 + i 2 )^ 5 + ( 3 2 - i 2 )^ 5 then
• Let α and β be the roots of equation px 2 + qx + r = 0, p ≠ 0 . If p, q, r are in A.P. and 1 + 1 =4, then the value of…
• If x=-5+2 -4 , then the value of x^ 4 +9 x^ 3 +35 x^ 2 -x+4 is -40 k . The value of is
• If α and β are the roots of the quadratic equations, x^ 2 +x -2 =0, (0, 2 ) , then a ^ 12 + ^ 12 ( a ^ -12 + ^ -12 ) (…
• If the difference between the roots of the equation x^ 2 +a x+1=0 is less than 5 . then the set of possible values of a…
• The roots of the quadratic equation x^ 2 -2 3 x-22=0 are
• If p, q, r be in HP and p and r be different having same sign, then the roots of the equation p x^ 2 +2 q x+r=0 will be
• If a, - a, b are the roots of x^ 3 -5 x^ 2 -x+5=0 , then b is a root of
• If and are the roots of then the value of is of the form . Then find the value of P.
• If a _ 1 are the roots of the equation x^ 2 +m x+n=0 , then the equation whose roots are x^ 3 and x^ 3 , is
• If z and w are two non-zero complex numbers such that |zw| = 1 and arg (z) – arg ( w )= 2 , then Z w is equal to
• If α and β are the roots of the quadratic equation, x 2 + x sinθ – 2 sinθ = 0, then is equal to
• If every pair from among the equations x ^ 2 +p x +q r=0 , x ^ 2 + x + p q =0 , x^ 2 +q x+r p=0 has a common root, then…
• If A(z 1 ), B(z 2 ), C(z 3 ) and P(z) represents complex numbers such that | z _ 1 - z |= | z _ 2 - z |= | z _ 3 - z |…
• The values of k for which the equations x 2 - kx - 21 = 0 and x 2 - 3kx + 35 = 0 will have a common root are
• If a,b,c are distinct real numbers then the equation (b-c) x^ 2 +(c-a) x+(a-b)=0 has
• The sum of the solutions of the equation | x -2|+ x ( x -4)+2=0,(x>0) is equal to:
• The principal amplitude of (sin 40 o + i cos 40 o ) 5 is
• If a, b ∈ R & the quadratic equation ax 2 – bx + 1 = 0 has imaginary roots then a + b + 1 is

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