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

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

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

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

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x^{3} - 27 i = 0

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

Solution steps

x^{3} - 27 i = 0

Move

27 i

to the right side

x^{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

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

3 x^{3} - 12 x^{2} + 3 x = 0

- 4 x^{3} + 24 x - 1 = 0

8 x^{3} - 48 x^{2} = 0

x^{3} + 2 x = 2

x^{4} + 4 x^{3} - 45 x^{2} = 0

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