Question

Resolva as operações de matemática abaixo com os números complexos e indique seus resultados.

A) z1=4-12i : z2=2+8=
B) z3=9i-z4=10-9i=
C) z5=5-3i-z6=40-3i=
D)z7=3+2i.z8=15-i=

Me ajudem é pra amanhã ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{z_1 = 4 -12i}$

$\mathsf{z_2 = 2 + 8i}$

$\mathsf{\dfrac{z_1}{z_2} = \dfrac{4 - 12i}{2 + 8i}}$

$\mathsf{\dfrac{4 - 12i}{2 + 8i}\times\dfrac{2 - 8i}{2 - 8i}}$

$\mathsf{\dfrac{8 - 32i - 24i + 96i^2}{4 - 64i^2}}$

$\mathsf{\dfrac{8 - 56i + 96(-1)}{4 - 64(-1)}}$

$\mathsf{\dfrac{8 - 56i - 96}{4 + 64}}$

$\mathsf{\dfrac{-88 - 56i}{68}}$

$\boxed{\boxed{\mathsf{\dfrac{z_1}{z_2} = -\dfrac{22}{17} -\dfrac{14i}{17}}}}$

$\mathsf{z_3 = 9i}$

$\mathsf{z_4 = 10 - 9i}$

$\mathsf{z_3 - z_4 = 9i - (10 - 9i) = -10 + 18i}$

$\boxed{\boxed{\mathsf{z_3 - z_4 = -10 + 18i}}}$

$\mathsf{z_5 = 5 - 3i}$

$\mathsf{z_6 = 40 - 3i}$

$\mathsf{z_5 - z_6 = (5 - 3i) - (40 - 3i) = 5 - 40 -3i + 3i = -35}$

$\boxed{\boxed{\mathsf{z_5 - z_6 = -35}}}$

$\mathsf{z_7 = 3 + 2i}$

$\mathsf{z_8 = 15 - i}$

$\mathsf{z_7.z_8 = (3 + 2i).(15 - i) = 45 - 3i + 30i - 2i^2 = 47 - 27i}$

$\boxed{\boxed{\mathsf{z_7.z_8 = 47 + 27i}}}$