Question

Modulus: If z1=-2+3i and z2=1+2i calculate, |z1|, |z2|, and |z1+2z2|

Answer 1

$|z_1|=\sqrt{(-2)^2+3^2}=\sqrt{4+9}=\sqrt{13}\\ |z_2|=\sqrt{1^2+2^2}=\sqrt{1+4}=\sqrt{5}\\\\ z_1+2z_2=-2+3i+2(1+2i)=-2+3i+2+4i=7i\\ |z_1+2z_2|=\sqrt{0^2+7^2}=7$