Question

calcule a multiplicação de números complexos abaixo :


(3 -2i). ( 4+3i)

(1+2i).(5-4i)

(3-i).(5i)

(1+1).(2-i)

Answer 1

Explicação passo-a-passo:

Sabendo que i é a unidade imaginária $i=\sqrt{-1}$ e $i^{2} =-1$.

a)

$Z=(3 -2i). ( 4+3i)\\\\Z=3.4+3.3i-2i.4-2i.3i\\\\Z=12+9i-8i-6i^{2} \\\\Z=12+i-6.(-1)\\\\Z=12+6+i\\\\Z=18+i$

b)

$Z=(1+2i).(5-4i)\\\\Z=1.5+1.(-4i)+2i.5+2i.(-4i)\\\\Z=5-4i+10i-8i^{2}\\ \\Z=5+6i-8.(-1)\\\\Z=5+8+6i\\\\Z=13+6i$

c)

$Z=(3-i).(5i)\\\\Z=3.5i-i.5i\\\\Z=15i-5i^{2} \\\\Z=15i-5.(-1)\\\\Z=5+15i$

d)

$Z=(1+1).(2-i)\\\\Z=2.(2-i)\\\\Z=2.2+2.(-i)\\\\Z=4-2i$