What are the solutions to the equation x^4=-2+2sqrt(3)i ?

The solutions to the equation x^4=-2+2sqrt(3)i are

Find the zeros of x^4=-2+2sqrt(3)i

The zeros of x^4=-2+2sqrt(3)i are

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x^{4} = - 2 + 23 i

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

Solution steps

x^{4} = - 2 + 23 i

For

z^{n} = a

the solutions are

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

For

n = 4, a = - 2 + 23 i

∣ a ∣ = 4

ar g (a) = - \frac{π}{3} + π

Simplify

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

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

9 x^{3} - 54 x^{2} - x + 6 = 0

23.92 x^{3} + 66.53 x^{2} - 300 = 0

z^{4} + 7 z^{2} - 144 = 0

3 x^{5} + 27 x^{3} = 0

What are the solutions to the equation x^4=-2+2sqrt(3)i ?
The solutions to the equation x^4=-2+2sqrt(3)i are
Find the zeros of x^4=-2+2sqrt(3)i
The zeros of x^4=-2+2sqrt(3)i are