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Complex Numbers question

2021 · 24 Feb · Shift 2 · Q38
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  5. /2021 · 24 Feb · Shift 2 · Q38

Complex Numbers question

2021 · 24 Feb · Shift 2 · Q38

JEE MainMathematicsComplex NumbersNumerical+4 / −1
Let i=−1i = \sqrt { - 1}i=−1​. If (−1+i3)21(1−i)24+(1+i3)21(1+i)24=k{{{{\left( { - 1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 - i)}^{24}}}} + {{{{\left( {1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 + i)}^{24}}}} = k(1−i)24(−1+i3​)21​+(1+i)24(1+i3​)21​=k, and n=[∣k∣]n = [|k|]n=[∣k∣] be the greatest integral part of | k |. Then ∑j=0n+5(j+5)2−∑j=0n+5(j+5)\sum\limits_{j = 0}^{n + 5} {{{(j + 5)}^2} - \sum\limits_{j = 0}^{n + 5} {(j + 5)} }j=0∑n+5​(j+5)2−j=0∑n+5​(j+5) is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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