How do you find all solutions to x^{4}-i=0?

Clarence Hines

Clarence Hines

Answered question

2022-02-01

How do you find all solutions to x4i=0?

Answer & Explanation

immablondevl

immablondevl

Beginner2022-02-02Added 11 answers

Step 1
Given: x4=i
it is better to express the immaginary unit in exponential form
i=eiπ2
in such a way we can rewrite the equation like this
x4=ei(π2+2kπ)
and as a consequence it must be
x=ei(π2+2kπ)4
=[ei(π2+2kπ)]14
=ei(π8+kπ2)
with k=0, 1, 2, 3

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