Question

2) Efetue:

a) ( 5 + 3i) .(2 + 4i)

b) ( 8 - 2i) . (4 +5i)

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

Answer 1

Explicação passo-a-passo:

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

a)

$Z=( 5 + 3i) .(2 + 4i)\\\\Z=5.2+5.4i+3i.2+3i.4i\\\\Z=10+20i+6i+12i^{2} \\\\Z=10+26i+12.(-1)\\\\Z=10-12+26i\\\\Z=-2+26i$

b)

$Z=( 8 - 2i) . (4 +5i)\\\\Z=8.4+8.5i-2i.4-2i.5i\\\\Z=32+40i-8i-10i^{2} \\\\Z=32+32i-10.(-1)\\\\Z=32+10+32i\\\\Z=42+32i$

c)

$Z=(-4 -4i) . (2 - 3i)\\\\Z=-4.2-4.(-3i)-4i.2-4i.(-3i)\\\\Z=-8+12i-8i+12i^{2} \\\\Z=-8+4i+12.(-1)\\\\Z=-8-12+4i\\\\Z=-20+4i$