What is the modulus of the complex number $(1+2 i)(-2+i)$ ?

Question

Aicharya · Accepted Answer

$\begin{aligned} \mid(\hat{i} & +2 \hat{i}) \cdot(-2+\hat{i})|=| \hat{i}+2 i|\cdot|-2+i \mid \ & =\left(\sqrt{1^2+2^2}\right) \cdot\left(\sqrt{(-2)^2+1^2}\right) \ & =\sqrt{5} \times \sqrt{5}=5 . \end{aligned}$

What is the modulus of the complex number \((1+2 i)(-2+i)\) ?

Solution