For positive integers

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

Problem

For positive integers n1,n2n_1, n_2 , the value of expression (1+i)n1+(1+i3)n1+(1+i5)n2+(1+i7)n2(1+i)^{n_1} + (1+i^3)^{n_1} + (1+i^5)^{n_2} + (1+i^7)^{n_2} , where i=−1i = \sqrt{-1} is a real number, if and only if (1) (B) n1=n2−1n_1 = n_2 - 1 (2) (A) n1=n2+1n_1 = n_2 + 1 (3) (D) n1>0,n2>0n_1 > 0, n_2 > 0 (4) (C) n1=n2n_1 = n_2

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