Question

3) Sejam os números complexos z_1 e z_2 , onde z_2=3i e z_1 .z_2= -9+6i. Então z_1+ z_2 vale:
(A QUESTÃO DEVE APRESENTAR SEUS RESPECTIVOS CÁLCULOS PARA SER VALIDADA)

a) 2 + 6 i
b) 2 - 6 i
c) -3 + 3 i
d) -3 - 3 i
e) 9 i

Answer 1

$\sf{Z_1\cdot Z_2=-9+6i}\\\sf{Z_1\cdot3i=-9+6i}\\\sf{Z_1=\dfrac{-9+6i}{3i}}\\\sf{Z_1=\dfrac{(-9+6i)}{3i}\cdot\dfrac{-3i}{-3i}}\\\sf{Z_1=\dfrac{27i-18i^2}{-9i^2}=\dfrac{18+27i}{9}=2+3i}\\\sf{Z_1+Z_2=2+3i+3i}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{Z_1+Z_2=2+6i}}}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\maltese~~alternativa~~a}}}}}$