What are the solutions to the equation z^3= 1/(8i) ?

The solutions to the equation z^3= 1/(8i) are z=(sqrt(3))/4-i 1/4 ,z=i 1/2 ,z=-(sqrt(3))/4-i 1/4

Find the zeros of z^3= 1/(8i)

The zeros of z^3= 1/(8i) are z=(sqrt(3))/4-i 1/4 ,z=i 1/2 ,z=-(sqrt(3))/4-i 1/4

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z^{3} = \frac{1}{8 i}

z = \frac{3}{4} - i \frac{1}{4}, z = i \frac{1}{2}, z = - \frac{3}{4} - i \frac{1}{4}

Solution steps

z^{3} = \frac{1}{8 i}

Simplify

\frac{1}{8 i} : - \frac{i}{8}

For

z^{n} = a

the solutions are

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

For

n = 3, a = - \frac{i}{8}

∣ a ∣ = \frac{1}{8}

ar g (a) = - \frac{π}{2}

Simplify

z = \frac{3}{4} - i \frac{1}{4}, z = i \frac{1}{2}, z = - \frac{3}{4} - i \frac{1}{4}

x^{3} - 8 x^{2} + 4 x = 32

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

2 y^{4} - 9 y^{3} + 14 y^{2} + 6 y - 63 = 0

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

5 z^{3} + 22 z^{2} = 15 z

What are the solutions to the equation z^3= 1/(8i) ?
The solutions to the equation z^3= 1/(8i) are z=(sqrt(3))/4-i 1/4 ,z=i 1/2 ,z=-(sqrt(3))/4-i 1/4
Find the zeros of z^3= 1/(8i)
The zeros of z^3= 1/(8i) are z=(sqrt(3))/4-i 1/4 ,z=i 1/2 ,z=-(sqrt(3))/4-i 1/4