What are the solutions to the equation z^3-27i=0 ?

The solutions to the equation z^3-27i=0 are z=(3sqrt(3))/2+i 3/2 ,z=-(3sqrt(3))/2+i 3/2 ,z=-3i

Find the zeros of z^3-27i=0

The zeros of z^3-27i=0 are z=(3sqrt(3))/2+i 3/2 ,z=-(3sqrt(3))/2+i 3/2 ,z=-3i

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z^{3} - 27 i = 0

z = \frac{3 3}{2} + i \frac{3}{2}, z = - \frac{3 3}{2} + i \frac{3}{2}, z = - 3 i

Solution steps

z^{3} - 27 i = 0

Move

27 i

to the right side

z^{3} = 27 i

For

z^{n} = a

the solutions are

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

For

n = 3, a = 27 i

∣ a ∣ = 27

ar g (a) = \frac{π}{2}

Simplify

z = \frac{3 3}{2} + i \frac{3}{2}, z = - \frac{3 3}{2} + i \frac{3}{2}, z = - 3 i

3 x^{4} - 5 x^{3} + 2 x - 1 = 0

b^{4} - 2 = 1

x^{3} - 21 x^{2} = 0

w^{3} = 81

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

What are the solutions to the equation z^3-27i=0 ?
The solutions to the equation z^3-27i=0 are z=(3sqrt(3))/2+i 3/2 ,z=-(3sqrt(3))/2+i 3/2 ,z=-3i
Find the zeros of z^3-27i=0
The zeros of z^3-27i=0 are z=(3sqrt(3))/2+i 3/2 ,z=-(3sqrt(3))/2+i 3/2 ,z=-3i