Question

Resoluções, pfv!
Gabarito: a) -4√2 + 4√2i, b) 16, c) -1024, d) -64

Answer 1

Olá!

letra (a)


(√2+√2i)^3=>

=>(√2+√2i)^2.(√2+√2i)

=>(√2)^2+2.(√2).(√2).i+(√2i)^2.(√2+√2i)

=>4i.(√2+√2i)

=>4√2i+4√2.(-1)

=>-4√2+4√2i

letra b)

(1-i)^8=>

=>((1-i)^2)^4

=>[(1-i).(1-i)]^4

=>(-2i)^4

=>(-2)^4.(i)^4

=>16.(i)

=>16.(i)^2+(i)^2

=>16.(-1).(-1)

=>16.1

=>16


letra C)

(4+4i)^4

=>((4+4i)^2)^2

=>[(4)^2+2.(4•4i)+(4i)^2]^2

=>[16+32-16]^2

=>[32i]^2

=>(32)^2.(i)^2

=> 1024.(-1)

=>-1024

letra d)


(1-i)^12=>


=>((1-i)^2)^6

=>[(1-i).(1-i)]^6

=>(1-2i-1)^6

=>(-2i)^6

=>(-2)^6.(i)^6

=>64.(-1)

=>-64


espero ter ajudado!

boa noite!