Question

determine o módulo de cada um dos seguintes números complexos Z = 3 + 4i Z = 3i e Z = 3 + 4i z= 3i z=3+4
$\sqrt{2} i$
z= 3+4 raiz quadrada de 2i z= - raiz quadrada de 2 - i raiz quadrada de 2

Answer 1

$\left|3+4i\right|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\\left|3i\right|=\sqrt{0^2+3^2}=\sqrt{9}=3\\\\\left|3+4\sqrt{2}i\right|=\sqrt{3^2+\left(4\sqrt{2}\right)^2}=\sqrt{9+16*2}=\sqrt{9+32}=\sqrt{41}\\\\\left|-\sqrt{2}-i\sqrt{2}\right|=\sqrt{\left(-\sqrt{2}\right)^2+\left(-\sqrt{2}\right)^2}=\sqrt{2+2}=\sqrt{4}=2$