What are the solutions to the equation ix^6-1=0 ?

The solutions to the equation ix^6-1=0 are

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ix^6-1=0

i x^{6} - 1 = 0

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

Solution steps

i x^{6} - 1 = 0

Move

1

to the right side

i x^{6} = 1

Divide both sides by

i

x^{6} = - i

For

z^{n} = a

the solutions are

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

For

n = 6, a = - i

∣ a ∣ = 1

ar g (a) = - \frac{π}{2}

Simplify

x = \frac{2 ( 1 + 3 )}{4} + i \frac{2 ( 1 - 3 )}{4}, x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2 ( 1 - 3 )}{4} + i \frac{2 ( 1 + 3 )}{4}, x = \frac{2 ( - 1 - 3 )}{4} + i \frac{2 ( - 1 + 3 )}{4}, x = - \frac{2}{2} - i \frac{2}{2}, x = \frac{2 ( - 1 + 3 )}{4} + i \frac{2 ( - 1 - 3 )}{4}

w^{3} - 2 w^{2} + w = 2

x^{6} + 7 2^{3} + 512 = 0

k^{3} = 8

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

(17 x - 11)^{3} - (17 x - 11) = 0

What are the solutions to the equation ix^6-1=0 ?
The solutions to the equation ix^6-1=0 are
Find the zeros of ix^6-1=0
The zeros of ix^6-1=0 are