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

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


Simplifying
z2 + -1(4 + i) * z + (5 + 5i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(4 + i) + (5 + 5i) = 0
z2 + (4 * -1z + i * -1z) + (5 + 5i) = 0

Reorder the terms:
z2 + (-1iz + -4z) + (5 + 5i) = 0
z2 + (-1iz + -4z) + (5 + 5i) = 0

Remove parenthesis around (5 + 5i)
z2 + -1iz + -4z + 5 + 5i = 0

Reorder the terms:
5 + 5i + -1iz + -4z + z2 = 0

Solving
5 + 5i + -1iz + -4z + z2 = 0

Solving for variable 'i'.

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

Add '-5' to each side of the equation.
5 + 5i + -1iz + -4z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + 5i + -1iz + -4z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5i + -1iz + -4z + z2 = 0 + -5
5i + -1iz + -4z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
5i + -1iz + -4z + z2 = -5

Add '4z' to each side of the equation.
5i + -1iz + -4z + 4z + z2 = -5 + 4z

Combine like terms: -4z + 4z = 0
5i + -1iz + 0 + z2 = -5 + 4z
5i + -1iz + z2 = -5 + 4z

Add '-1z2' to each side of the equation.
5i + -1iz + z2 + -1z2 = -5 + 4z + -1z2

Combine like terms: z2 + -1z2 = 0
5i + -1iz + 0 = -5 + 4z + -1z2
5i + -1iz = -5 + 4z + -1z2

Reorder the terms:
5 + 5i + -1iz + -4z + z2 = -5 + 4z + -1z2 + 5 + -4z + z2

Reorder the terms:
5 + 5i + -1iz + -4z + z2 = -5 + 5 + 4z + -4z + -1z2 + z2

Combine like terms: -5 + 5 = 0
5 + 5i + -1iz + -4z + z2 = 0 + 4z + -4z + -1z2 + z2
5 + 5i + -1iz + -4z + z2 = 4z + -4z + -1z2 + z2

Combine like terms: 4z + -4z = 0
5 + 5i + -1iz + -4z + z2 = 0 + -1z2 + z2
5 + 5i + -1iz + -4z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
5 + 5i + -1iz + -4z + z2 = 0

The solution to this equation could not be determined.

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