What are the solutions to the equation z^3=(-5sqrt(3)+5i)^3 ?

The solutions to the equation z^3=(-5sqrt(3)+5i)^3 are z=5sqrt(3)+5i,z=-5sqrt(3)+5i,z=-10i

Find the zeros of z^3=(-5sqrt(3)+5i)^3

The zeros of z^3=(-5sqrt(3)+5i)^3 are z=5sqrt(3)+5i,z=-5sqrt(3)+5i,z=-10i

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z^{3} = (- 53 + 5 i)^{3}

z = 53 + 5 i, z = - 53 + 5 i, z = - 10 i

Solution steps

z^{3} = (- 53 + 5 i)^{3}

Simplify

(- 53 + 5 i)^{3} : 1000 i

For

z^{n} = a

the solutions are

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

For

n = 3, a = 1000 i

∣ a ∣ = 1000

ar g (a) = \frac{π}{2}

Simplify

z = 53 + 5 i, z = - 53 + 5 i, z = - 10 i

2 x^{3} - 2 x^{2} - 16 x = 2 x^{2}

- λ^{3} + 3 λ^{2} + 9 λ + 5 = 0

- x^{3} + 4 x^{2} + 25 x - 100 = 0

9 = x^{5} + x^{3} + x

3 x^{3} - 4 x^{2} - 48 x + 64 = 0

What are the solutions to the equation z^3=(-5sqrt(3)+5i)^3 ?
The solutions to the equation z^3=(-5sqrt(3)+5i)^3 are z=5sqrt(3)+5i,z=-5sqrt(3)+5i,z=-10i
Find the zeros of z^3=(-5sqrt(3)+5i)^3
The zeros of z^3=(-5sqrt(3)+5i)^3 are z=5sqrt(3)+5i,z=-5sqrt(3)+5i,z=-10i