For positive integers n 1 , n 2 the value of expression (1+ i )^ n _ 1 + (1+ i ^ 3 )^ n _…
Mathematics · JEE Main · NTA Exams — Complex Numbers and Quadratic Equations
For positive integers n1, n2 the value of expression \((1+\mathrm{i})^{\mathrm{n}_{1}}+\left(1+\mathrm{i}^{3}\right)^{\mathrm{n}_{1}}+\left(1+\mathrm{i}^{5}\right)^{\mathrm{n}_{2}}+\left(1+\mathrm{i}^{7}\right)^{\mathrm{n}_{2}},\) here \(i=\sqrt{-1}\) is a real number, if and only if
- n1 = n2 + 1
- n1 = n2 – 1
- n1 = n2
- n1 > 0, n2 > 0
Answer
(D) n 1 > 0, n 2 > 0
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