Let i= -1 . If (-1+i 3 )^ 21 (1-i)^ 24 + (1+i 3 )^ 21 (1+i)^ 24 =k, and n=[|k|] be the…
Mathematics · JEE Main · NTA Exams — Complex Numbers and Quadratic Equations
Let \(i=\sqrt{-1} .\) If \[\frac{(-1+i \sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i \sqrt{3})^{21}}{(1+i)^{24}}=k,\] and \(n=[|k|]\) be the greatest integral part of 
Then \(\sum_{j=0}^{n+5}(j+5)^{2}-\sum_{j=0}^{n+5}(j+5)\) is equal to ___.
Then \(\sum_{j=0}^{n+5}(j+5)^{2}-\sum_{j=0}^{n+5}(j+5)\) is equal to ___.- \(310\)
- \(280\)
- \(330\)
- \(250\)
Answer
(A) 310
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