JEE Mains · Maths · STD 11 - 4.1 complex nubers
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 \(| k |\). Then \(\sum_{ j =0}^{ n +5}( j +5)^{2}-\sum_{ j =0}^{ n +5}( j +5)\) is equal to ........ .
- A \(620\)
- B \(310\)
- C \(155\)
- D \(280\)
Answer & Solution
Correct Answer
(B) \(310\)
Step-by-step Solution
Detailed explanation
\(K=\frac{1}{2^{9}}\left[\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)^{21}}{\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}} i \right)^{24}}+\frac{\left(\frac{1}{2}+\frac{ i \sqrt{3}}{2}\right)^{21}}{\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} i \right)^{24}}\right]\)…
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