Let and . Suppose , where . If and , then lies…

MATHEMATICS · Subjective · AoPS · Mathematics · Complex Numbers · Complex Numbers

Problem

Let

a,b\in\mathbb{R}

and

a^2+b^2\ne0

. Suppose

S=\left\{z\in\mathbb{C}:z=\frac{t}{a+ib},\ t\in\mathbb{R},\ t\ne0\right\}

, where

i=\sqrt{-1}

. If

z=x+iy

and

z\in S

, then

(x,y)

lies on:

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