Question

Sejam z1=2-6i e z2=3+5i,efetue:
A)z1+z2

B)z1-z2

C)z1× z2

D)z1÷z2

Answer 1

Resposta:

Explicação passo-a-passo:

a)

z₁ + z₂ = 2 - 6i + 3 + 5i = 2 + 3 -6i + 5i = 5 - i

b)

z₁ - z₂ = 2 - 6i - (3 + 5i) = 2 - 6i - 3 - 5i = 2 - 3 - 6i -5i = -1 - 11i

c)

z₁ x  z₂= (2 - 6i)(3 + 5i) = 2.3 + 2(-6i) - 6i.3 - 6i.5i = 6 - 12i - 18i - 30i² = 6 - 30i - 30(-1) = 6 - 30i + 30 = 36 - 30i

d)

$\frac{z_{1}}{z_{2}}=\frac{2-6i}{3+5i}=\frac{(2-6i)(3-5i)}{(3+5i)(3-5i)}=\frac{2.3-2.5i-6i.3-6i.(-5i)}{3^{2}-(5i)^{2}}=\frac{6-10i-18i+30i^{2}}{9-25i^{2}}=\frac{6-28i-30}{6+25}=\frac{-24-28i}{31}=-\frac{24}{31}-\frac{28i}{31}$