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

The solutions to the equation z^3+i=0 are z=(sqrt(3))/2-i 1/2 ,z=i,z=-(sqrt(3))/2-i 1/2

Find the zeros of z^3+i=0

The zeros of z^3+i=0 are z=(sqrt(3))/2-i 1/2 ,z=i,z=-(sqrt(3))/2-i 1/2

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z^{3} + i = 0

z = \frac{3}{2} - i \frac{1}{2}, z = i, z = - \frac{3}{2} - i \frac{1}{2}

Solution steps

z^{3} + i = 0

Move

i

to the right side

z^{3} = - i

For

z^{n} = a

the solutions are

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

For

n = 3, a = - i

∣ a ∣ = 1

ar g (a) = - \frac{π}{2}

Simplify

z = \frac{3}{2} - i \frac{1}{2}, z = i, z = - \frac{3}{2} - i \frac{1}{2}

x^{4} - 2 x^{2} - 63 = 0

3 x - 2 = x^{8}

x^{5} = 32

x^{3} - 4 x^{2} + 6 x - 5 = 0

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

What are the solutions to the equation z^3+i=0 ?
The solutions to the equation z^3+i=0 are z=(sqrt(3))/2-i 1/2 ,z=i,z=-(sqrt(3))/2-i 1/2
Find the zeros of z^3+i=0
The zeros of z^3+i=0 are z=(sqrt(3))/2-i 1/2 ,z=i,z=-(sqrt(3))/2-i 1/2