Question

Expresse z na forma algebrica.
a) z=(1+i/1-i)^2
b) z=3(1+i/1-i) - 2-4i/1+i

Answer 1

Boa noite Jordana 

a)

(1 + i)/(1 - i) = (1 + i)*(1 + i)/((1 - i)*(1 + i))

(1 + i + i -1)/(1 + 1) = 2i/2 = i

z = i² = -1 

b) 

(2 - 4i)/(1 + i) = (2 - 4i)*(1 - i)/((1 + i)*(1 - i)) 

(2 - 2i - 4i - 4)/(1 + 1) = (-2 - 6i)/2 = -1 - 3i

z = 3i - (-1 - 3i) = 1 + 6i