Question

If z is a complex number of unit modulus, the value of $\frac{2+2z}{3+3\overline{z}}$ is

• A.
• B.
• C. z
• D. None of these

Answer 1

The correct option is B

Given |z| = 1

$\Rightarrow$ $|z{|}^2$ = z $\overline{z}$ = 1

$\Rightarrow$ $\overline{z}$ = $\frac{1}{z}$

$\frac{2+2z}{3+3\overline{z}}$ = $\frac{2[1+z]}{3[1+\overline{z}]}$ = $\frac{2}{3}\frac{1+z}{1+\frac{1}{z}}$

= $\frac{2}{3}\frac{1+z}{\left(\frac{1+z}{z}\right)}$
= $\frac{2}{3}$ z