What are the solutions to the equation z^3+8i=0 ?

The solutions to the equation z^3+8i=0 are z=sqrt(3)-i,z=2i,z=-sqrt(3)-i

Find the zeros of z^3+8i=0

The zeros of z^3+8i=0 are z=sqrt(3)-i,z=2i,z=-sqrt(3)-i

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z^{3} + 8 i = 0

z = 3 - i, z = 2 i, z = - 3 - i

Solution steps

z^{3} + 8 i = 0

Move

8 i

to the right side

z^{3} = - 8 i

For

z^{n} = a

the solutions are

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

For

n = 3, a = - 8 i

∣ a ∣ = 8

ar g (a) = - \frac{π}{2}

Simplify

z = 3 - i, z = 2 i, z = - 3 - i

x (x^{2} - 16) = 0

x^{4} - 5 x^{2} + 6 = 0

x^{3} = 350

(x + 1)^{4} + (x + 5)^{4} = 32

x^{3} - 3 x - 2 = 0

What are the solutions to the equation z^3+8i=0 ?
The solutions to the equation z^3+8i=0 are z=sqrt(3)-i,z=2i,z=-sqrt(3)-i
Find the zeros of z^3+8i=0
The zeros of z^3+8i=0 are z=sqrt(3)-i,z=2i,z=-sqrt(3)-i