Question

The modulus of the complex number is $\left(\frac{6+8i}{1-2i}\right)$

• A. $2\sqrt{5}$
• B. $\sqrt{5}$
• C. $\frac{\sqrt{5}}{2}$
• D. $\frac{2}{\sqrt{5}}$

Answer 1

The correct option is A $2\sqrt{5}$

$z=\frac{6+8i}{1-2i}=\frac{(6+8i)(1+2i)}{(1-2i)(1+2i)}$
$=\frac{-10+20i}{5}=-2+4i$
$|z|=\sqrt{(-2{)}^2+(4{)}^2}=2\sqrt{5}$