Question

Números complexos
Dados os números complexos z¹=(1,2), z²=(-1,3) e z³=(2,-2), calcule:
a)     Z¹ +Z²
b)   ( Z¹ +Z²)Z³
c)   Z1² + Z2
d)   Z2¹ +Z3² - Z1² 

Answer 1

Olá, GPB.

 

$<var>z_1=1+2i, z_2=-1+3i, z_3=2-2i\\\\ a)z_1+z_2=1+2i-1+3i=5i=(0,5)\\\\ b)(z_1+z_2)z_3=5i(2-2i)=10i-10i^2=10i-10(-1)=10i+10\\=10+10i=(10,10)\\\\</var>$

 

$<var>c)z_1^2 + z_2=(1+2i)^2-1+3i=1+4i+4i^2-1+3i=\\4(-1)+7i=-4+7i=(-4,7)\\\\ d)z_2^2+z_3^2-z_1^2=(-1+3i)^2+(2-2i)^2-(1+2i)^2=\\1-6i-9+4-8i-4-(1+4i-4)=-5-18i=(-5,-18) </var>$