A complex number z is said to be unimodular if |z|=1.

Question

A complex number $z$ is said to be unimodular if $|z|=1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\dfrac{z_1-2z_2}{2-z_1\bar z_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:

Accepted Answer

Setting the modulus-squared equal to 1 and expanding, $(|z_1|^2-4)(1-|z_2|^2)=0$. Since $|z_2|
e1$, $|z_1|^2=4 \implies |z_1|=2$, a circle of radius 2.

Solutions · 1