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=3i,z=-(3sqrt(3))/2-i 3/2

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

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

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z^{3} + 27 i = 0

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

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

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

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

x^{3} - 10 x^{2} + 9 x = 0

x^{3} - 12 x - 5 = 0

x^{6} = 9^{- 3}

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