Question

calcule o modulo dos numeros complexos:
z=6-2i/2+i x 1/i​

Answer 1

Resposta:

|Z|=2√2

Explicação passo-a-passo:

$\displaystyle z=\frac{6-2i}{2+i} .\frac{1}{i} =\frac{6-2i}{2i+i^{2}} =\frac{6-2i}{-1+2i}.\frac{(-1-2i)}{(-1-2i)} =\frac{-6-12i+2i+4i^{2}}{1-4i^{2}}=\\\\\frac{-6-10i-4}{1+4}=-\frac{10+10i}{5}=-2-2i \\\\\\|Z|=\sqrt{(-2)^{2}+(-2)^{2}}=\sqrt{2.4}=2\sqrt{2}$