Por favor preciso de ajuda rapido, é de numeros complexos. obrigado.
(1/2 + 1/2i)^100 =
(1/2 + 1/2i)^(2 * 50) =
abrindo:
[(1/2 + 1/2i) ^ 2]^50 =
[1/4 + 2 * 1/2 * i/2 + 1/4 i²]^50 =
( i / 2 ) ^ 50 =
resolvendo:
i^50 / 2^50 =
(i^2)^25 / 2^50 =
(-1) ^25 / 2^50
-1 / 2^50 =
-2^(-50)
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Verified answer
(1/2 + 1/2i)^100 =
(1/2 + 1/2i)^(2 * 50) =
abrindo:
[(1/2 + 1/2i) ^ 2]^50 =
[1/4 + 2 * 1/2 * i/2 + 1/4 i²]^50 =
( i / 2 ) ^ 50 =
resolvendo:
i^50 / 2^50 =
(i^2)^25 / 2^50 =
(-1) ^25 / 2^50
-1 / 2^50 =
-2^(-50)