Z^4-(4+2i)z+8i=0

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Solution for Z^4-(4+2i)z+8i=0 equation: 


Simplifying
Z4 + -1(4 + 2i) * z + 8i = 0

Reorder the terms for easier multiplication:
Z4 + -1z(4 + 2i) + 8i = 0
Z4 + (4 * -1z + 2i * -1z) + 8i = 0

Reorder the terms:
Z4 + (-2iz + -4z) + 8i = 0
Z4 + (-2iz + -4z) + 8i = 0

Reorder the terms:
Z4 + 8i + -2iz + -4z = 0

Solving
Z4 + 8i + -2iz + -4z = 0

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '-8i' to each side of the equation.
Z4 + 8i + -2iz + -8i + -4z = 0 + -8i

Reorder the terms:
Z4 + 8i + -8i + -2iz + -4z = 0 + -8i

Combine like terms: 8i + -8i = 0
Z4 + 0 + -2iz + -4z = 0 + -8i
Z4 + -2iz + -4z = 0 + -8i
Remove the zero:
Z4 + -2iz + -4z = -8i

Add '2iz' to each side of the equation.
Z4 + -2iz + 2iz + -4z = -8i + 2iz

Combine like terms: -2iz + 2iz = 0
Z4 + 0 + -4z = -8i + 2iz
Z4 + -4z = -8i + 2iz

Add '4z' to each side of the equation.
Z4 + -4z + 4z = -8i + 2iz + 4z

Combine like terms: -4z + 4z = 0
Z4 + 0 = -8i + 2iz + 4z
Z4 = -8i + 2iz + 4z

Simplifying
Z4 = -8i + 2iz + 4z

Reorder the terms:
Z4 + 8i + -2iz + -4z = -8i + 8i + 2iz + -2iz + 4z + -4z

Combine like terms: -8i + 8i = 0
Z4 + 8i + -2iz + -4z = 0 + 2iz + -2iz + 4z + -4z
Z4 + 8i + -2iz + -4z = 2iz + -2iz + 4z + -4z

Combine like terms: 2iz + -2iz = 0
Z4 + 8i + -2iz + -4z = 0 + 4z + -4z
Z4 + 8i + -2iz + -4z = 4z + -4z

Combine like terms: 4z + -4z = 0
Z4 + 8i + -2iz + -4z = 0

The solution to this equation could not be determined.

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