Question

If $z$ is a complex number such that $|z|=1$, then $\left|\frac{1}{\overline{z}}\right|$ is

• A. $0$
• B. $-1$
• C. $\sqrt{2}$
• D. $1$

Answer 1

The correct option is D $1$

Let $z=x+iy|z|=\sqrt{x^2+y^2}=1x^2+y^2=1\frac{1}{z}=\frac{1}{x+iy}\frac{x-iy}{\sqrt{x^2+y^2}}=x-iy\left|\frac{1}{z}\right|=\sqrt{x^2+y^2}=1$