If and are non-zero complex numbers such that and

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

Problem

z_1

and

z_2

are non-zero complex numbers such that

\frac{z_1}{z_2}+\frac{\overline{z}_1}{\overline{z}_2}=2

and

\frac{z_1}{z_2}-\frac{\overline{z}_1}{\overline{z}_2}=2i

, where

\overline{z}

denotes the conjugate of

z

and

i=\sqrt{-1}

, identify the correct statements. (A) The origin,

z_1

, and

z_2

form a right-angled triangle at

z_2

. (B) The origin,

z_1

, and

z_2

form a right-angled triangle at the origin. (C)

|z_1|=|z_2|

. (D)

|z_2|=|z_1-z_2|