What are the solutions to the equation z^4=8sqrt(2)+8sqrt(2)i ?

The solutions to the equation z^4=8sqrt(2)+8sqrt(2)i are

Find the zeros of z^4=8sqrt(2)+8sqrt(2)i

The zeros of z^4=8sqrt(2)+8sqrt(2)i are

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z^{4} = 82 + 82 i

z = 2 + 2 + 2 + i 2 - 2 + 2, z = - 2 - 2 + 2 + i 2 + 2 + 2, z = - 2 + 2 + 2 - i 2 - 2 + 2, z = 2 - 2 + 2 - i 2 + 2 + 2

Solution steps

z^{4} = 82 + 82 i

For

z^{n} = a

the solutions are

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

For

n = 4, a = 82 + 82 i

∣ a ∣ = 16

ar g (a) = \frac{π}{4}

Simplify

z = 2 + 2 + 2 + i 2 - 2 + 2, z = - 2 - 2 + 2 + i 2 + 2 + 2, z = - 2 + 2 + 2 - i 2 - 2 + 2, z = 2 - 2 + 2 - i 2 + 2 + 2

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

x^{3} - 7 x^{2} + 4 x + 30 = 0

2 x^{4} + 5 x^{2} + 2 = 0

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

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

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