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

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

Find the zeros of z^3=8i

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

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z^{3} = 8 i

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

Solution steps

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 = - 3 + i, z = - 2 i

x^{3} - 3 x^{2} - 3 x - 1 = 0

g^{5} = 0.536

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

x^{3} + x - 6 = 0

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

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