If are positive integers

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

If n1,n2n_1, n_2 are positive integers, then (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} is a real number if and only if

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