find all solutions to x^4+(1+i)=0.

enartartdn

enartartdn

Answered question

2023-02-01

find all solutions to x 4 + ( 1 + i ) = 0

Answer & Explanation

Magdalena Anthony

Magdalena Anthony

Beginner2023-02-02Added 6 answers

e i ϕ = cos ϕ + i sin ϕ
- ( 1 + i ) = - 2 ( 1 2 + i 2 ) = - 2 ( cos ϕ 0 + i sin ϕ 0 ) with ϕ 0 = π 4 + 2 k π , k = 0 , ± 1 , ± 2 ,
- 2 ( cos ϕ 0 + i sin ϕ 0 ) = 2 e i π e i ( π 4 + 2 k π ) = 2 e i ( 5 4 π + 2 k π )
x 4 = 2 e i ( 5 4 π + 2 k π )
x = 2 8 e i ( 5 16 π + k π 2 ) for k = 0 , ± 1 , ± 2 ,
Neuwiedlq8

Neuwiedlq8

Beginner2023-02-03Added 1 answers

In this case autor used the Moivre's identity

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