Question

Modulus of $\left(\frac{3+2i}{3-2i}\right)$ is
[RPET 1996]

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

Answer 1

The correct option is A 1

$\left(\frac{3+2i}{3-2i}\right)=\left(\frac{3+2i}{3-2i}\right)\left(\frac{3+2i}{3+2i}\right)=\frac{9-4+12i}{13}=\frac{5}{13}+\left(\frac{12}{13}\right)$
Modulus $=\sqrt{{\left(\frac{5}{13}\right)}^2+{\left(\frac{12}{13}\right)}^2=1}.$