Question

Number of complex numbers $z$ such that $|z|=1$ and $|\frac{z}{z}+\frac{\overline{z}}{z}|=1$ is

• A. $4$
• B. $1$
• C. $8$
• D. $morethen8$

Answer 1

The correct option is B $1$

Since $z$ is equidistant from $1,-1,i$, we can say that $z$is center of circle with $1,-1,i$ lying on it's circumference and so there is one one circle possible passing through $3$ points. So, the answer is $1$.