Z^2-z(4+3i)+1+5i=0

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Solution for Z^2-z(4+3i)+1+5i=0 equation: 


Simplifying
Z2 + -1z(4 + 3i) + 1 + 5i = 0
Z2 + (4 * -1z + 3i * -1z) + 1 + 5i = 0

Reorder the terms:
Z2 + (-3iz + -4z) + 1 + 5i = 0
Z2 + (-3iz + -4z) + 1 + 5i = 0

Reorder the terms:
1 + Z2 + 5i + -3iz + -4z = 0

Solving
1 + Z2 + 5i + -3iz + -4z = 0

Solving for variable 'Z'.

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

Add '-1' to each side of the equation.
1 + Z2 + 5i + -3iz + -1 + -4z = 0 + -1

Reorder the terms:
1 + -1 + Z2 + 5i + -3iz + -4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + Z2 + 5i + -3iz + -4z = 0 + -1
Z2 + 5i + -3iz + -4z = 0 + -1

Combine like terms: 0 + -1 = -1
Z2 + 5i + -3iz + -4z = -1

Add '-5i' to each side of the equation.
Z2 + 5i + -3iz + -5i + -4z = -1 + -5i

Reorder the terms:
Z2 + 5i + -5i + -3iz + -4z = -1 + -5i

Combine like terms: 5i + -5i = 0
Z2 + 0 + -3iz + -4z = -1 + -5i
Z2 + -3iz + -4z = -1 + -5i

Add '3iz' to each side of the equation.
Z2 + -3iz + 3iz + -4z = -1 + -5i + 3iz

Combine like terms: -3iz + 3iz = 0
Z2 + 0 + -4z = -1 + -5i + 3iz
Z2 + -4z = -1 + -5i + 3iz

Add '4z' to each side of the equation.
Z2 + -4z + 4z = -1 + -5i + 3iz + 4z

Combine like terms: -4z + 4z = 0
Z2 + 0 = -1 + -5i + 3iz + 4z
Z2 = -1 + -5i + 3iz + 4z

Simplifying
Z2 = -1 + -5i + 3iz + 4z

Reorder the terms:
1 + Z2 + 5i + -3iz + -4z = -1 + -5i + 3iz + 4z + 1 + 5i + -3iz + -4z

Reorder the terms:
1 + Z2 + 5i + -3iz + -4z = -1 + 1 + -5i + 5i + 3iz + -3iz + 4z + -4z

Combine like terms: -1 + 1 = 0
1 + Z2 + 5i + -3iz + -4z = 0 + -5i + 5i + 3iz + -3iz + 4z + -4z
1 + Z2 + 5i + -3iz + -4z = -5i + 5i + 3iz + -3iz + 4z + -4z

Combine like terms: -5i + 5i = 0
1 + Z2 + 5i + -3iz + -4z = 0 + 3iz + -3iz + 4z + -4z
1 + Z2 + 5i + -3iz + -4z = 3iz + -3iz + 4z + -4z

Combine like terms: 3iz + -3iz = 0
1 + Z2 + 5i + -3iz + -4z = 0 + 4z + -4z
1 + Z2 + 5i + -3iz + -4z = 4z + -4z

Combine like terms: 4z + -4z = 0
1 + Z2 + 5i + -3iz + -4z = 0

The solution to this equation could not be determined.

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