Question

Calcule:
a) (1+i)⁵
b) (1+i√3)⁸

Ajudem pf​

Answer 1

Resposta:

A)

$- 4 - 4i$

A

$256(cos( \frac{2\pi}{3?} + 2\pi) + i \times sin( \frac{2\pi}{3?} + 2\pi))$

Answer 2

i²=[√(-1)]²=-1

a) (1+i)⁵  =[(1+i)²]² *(1+i)

=[1+2i+i²]² *(1+i)

=[1+2i+-1]² *(1+i)  

=(2i)²*(1+i)

=2²*i²*(1+i)

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

b) (1+i√3)⁸ =[(1+i√3)²]⁴

=[1+2i√3+(i√3)²]⁴

=[1+2i√3+3*i²]⁴

=[1+2i√3-3]⁴

=[2i√3-2]⁴

=2⁴ *[(i√3-1)²]²

=16 *[-3-2i√3+1]²

=16 *[-2-2i√3]²

=16 *2² *(-1-i√3)²

=64*(1+2i√3-3)

=64*(2i√3-2)

= -128+128i√3