Question

If $z=\frac{\sqrt{3}}{2}+\frac{1}{2}i$ then $z\overline{z}$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

Conjugate of $\frac{\sqrt{3}+i}{2}=\frac{\sqrt{3}-i}{2}$

$\therefore \overline{z}=\frac{\sqrt{3}-i}{2}$

Now,$z\overline{z}=\left(\frac{\sqrt{3}+i}{2}\right)\left(\frac{\sqrt{3}-i}{2}\right)=\frac{3-i^2}{4}=\frac{3+1}{4}=\frac{4}{4}=1$