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

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

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

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

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

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

Solution steps

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

For

z^{n} = a

the solutions are

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

For

n = 3, a = \frac{1}{8} i

∣ a ∣ = \frac{1}{8}

ar g (a) = \frac{π}{2}

Simplify

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

49 x^{4} - 25 x^{2} = 0

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

r^{4} + 9 r^{2} = 0

x (x - 2)^{2} - 3 = 7

2 x^{3} - 15 x^{2} + 27 x - 10 = 0

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