Question

The modulus of the complex number$\left(\frac{6i-3}{12i+9}\right)$ is

• A. $5$
• B. $\sqrt{5}$
• C. $\frac{1}{5}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{5}}$

$Z=\frac{6i-3}{12i+9}=\frac{2i-1}{4i+3}$

$=\frac{(2i-1)(4i-3)}{(4i+3)(4i-3)}=\frac{-5-10i}{-25}=\frac{1}{5}+\frac{2i}{5}$

$|Z|=\sqrt{{\left(\frac{1}{5}\right)}^2+{\left(\frac{2}{5}\right)}^2}=\frac{1}{\sqrt{5}}$