What are the solutions to the equation z^4-i=0 ?

The solutions to the equation z^4-i=0 are

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z^4-i=0

z^{4} - i = 0

z = \frac{2 + 2}{2} + i \frac{2 - 2}{2}, z = - \frac{2 - 2}{2} + i \frac{2 + 2}{2}, z = - \frac{2 + 2}{2} - i \frac{2 - 2}{2}, z = \frac{2 - 2}{2} - i \frac{2 + 2}{2}

Solution steps

z^{4} - i = 0

Move

i

to the right side

z^{4} = i

For

z^{n} = a

the solutions are

k = 0, 1, \dots, n - 1

For

n = 4, a = i

∣ a ∣ = 1

ar g (a) = \frac{π}{2}

Simplify

z = \frac{2 + 2}{2} + i \frac{2 - 2}{2}, z = - \frac{2 - 2}{2} + i \frac{2 + 2}{2}, z = - \frac{2 + 2}{2} - i \frac{2 - 2}{2}, z = \frac{2 - 2}{2} - i \frac{2 + 2}{2}

x, y = x^{3}

4 x^{4} - 37 x^{2} + 9 = 0

27 x^{3} - 343 = 0

(2 x - 5) (3 x^{2} + 7 x - 6) = 0

- x^{3} + 4 x^{2} - 5 x + 2 = 0

What are the solutions to the equation z^4-i=0 ?
The solutions to the equation z^4-i=0 are
Find the zeros of z^4-i=0
The zeros of z^4-i=0 are