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

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

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

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x^{3} + 27 i = 0

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

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

y^{4} - 7 y^{3} - 18 y^{2} = 0

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

x, x^{3} - 7 x^{2} = 7 - x

x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 = 0

12 x^{3} - 6 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=3i,x=-(3sqrt(3))/2-i 3/2
Find the zeros of x^3+27i=0
The zeros of x^3+27i=0 are x=(3sqrt(3))/2-i 3/2 ,x=3i,x=-(3sqrt(3))/2-i 3/2