Question

Agora faça você!
a) z = (1 + i)20
b) z=(1 – 21) 8​

Answer 1

Resposta:

a)

z = (1 + i)²⁰ =[(1+i)²]¹⁰

=[1+2i+i²]¹⁰

=[1+2i-1]¹⁰

=(2i)¹⁰

=2¹⁰ *i¹⁰

=1024*(i²)⁵

=1024*(-1)⁵

= -1024

b)

z=(1 – 2i)⁸​=[(1-2i)²]⁴

=[1-4i+(2i)²]⁴

=[1-4i+4i²]⁴

=[1-4i-4]⁴

=[-3-4i]⁴ = [3+4i]⁴

=[3+4i]²  * [3+4i]²

=(9+24i+16i²)*(9+24i+16i²)

=(9+24i-16)*(9+24i-16)

=(24i-7)*(24i-7)

=24²*i² -7*24i -7*24i+49

=-576-336i+49

= -527-336i