What are the solutions to the equation Z^3+4=5+i ?

The solutions to the equation Z^3+4=5+i are

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Z^3+4=5+i

Z^{3} + 4 = 5 + i

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

Solution steps

Z^{3} + 4 = 5 + i

Move

4

to the right side

Z^{3} = 1 + i

For

z^{n} = a

the solutions are

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

For

n = 3, a = 1 + i

∣ a ∣ = 2

ar g (a) = \frac{π}{4}

Simplify

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

x^{6} - 10 x^{3} + 24 = 0

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

x^{3} - 3 x^{2} + 3 x - 65 = 0

(x^{2} + 6)^{2} = 0

32 = 4 x^{3}

What are the solutions to the equation Z^3+4=5+i ?
The solutions to the equation Z^3+4=5+i are
Find the zeros of Z^3+4=5+i
The zeros of Z^3+4=5+i are