Let i=√−1. If (−1+i√3)21(1−i)24+(1+i√3)21(1+i)24=k, and n= – InterviewSolution

1.	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 \|k\|. Then n+5∑j=0(j+5)2−n+5∑j=0(j+5) is equal to
Answer» 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 $n + 5 \sum j = 0 (j + 5)^{2} - n + 5 \sum j = 0 (j + 5)$ is equal to

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