If the equation ( z- ((-1- 3 )+(1+ 3 )i ) 2 2 )^n=1- ( z 2 )^n has a solution

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

If the equation (z−((−1−3)+(1+3)i)22)n=1−(z2)n\left(\frac{z-\left((-1-\sqrt{3})+(1+\sqrt{3})i\right)}{2\sqrt{2}}\right)^n=1-\left(\frac{z}{2}\right)^n has a solution, then nn must be a multiple of (A) 3 (B) 4 (C) 1 (D) 6

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