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

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


Simplifying
Z2 + (5 + -2i) * z + 1 + 3i = 0

Reorder the terms for easier multiplication:
Z2 + z(5 + -2i) + 1 + 3i = 0
Z2 + (5 * z + -2i * z) + 1 + 3i = 0

Reorder the terms:
Z2 + (-2iz + 5z) + 1 + 3i = 0
Z2 + (-2iz + 5z) + 1 + 3i = 0

Reorder the terms:
1 + Z2 + 3i + -2iz + 5z = 0

Solving
1 + Z2 + 3i + -2iz + 5z = 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 + 3i + -2iz + -1 + 5z = 0 + -1

Reorder the terms:
1 + -1 + Z2 + 3i + -2iz + 5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + Z2 + 3i + -2iz + 5z = 0 + -1
Z2 + 3i + -2iz + 5z = 0 + -1

Combine like terms: 0 + -1 = -1
Z2 + 3i + -2iz + 5z = -1

Add '-3i' to each side of the equation.
Z2 + 3i + -2iz + -3i + 5z = -1 + -3i

Reorder the terms:
Z2 + 3i + -3i + -2iz + 5z = -1 + -3i

Combine like terms: 3i + -3i = 0
Z2 + 0 + -2iz + 5z = -1 + -3i
Z2 + -2iz + 5z = -1 + -3i

Add '2iz' to each side of the equation.
Z2 + -2iz + 2iz + 5z = -1 + -3i + 2iz

Combine like terms: -2iz + 2iz = 0
Z2 + 0 + 5z = -1 + -3i + 2iz
Z2 + 5z = -1 + -3i + 2iz

Add '-5z' to each side of the equation.
Z2 + 5z + -5z = -1 + -3i + 2iz + -5z

Combine like terms: 5z + -5z = 0
Z2 + 0 = -1 + -3i + 2iz + -5z
Z2 = -1 + -3i + 2iz + -5z

Simplifying
Z2 = -1 + -3i + 2iz + -5z

Reorder the terms:
1 + Z2 + 3i + -2iz + 5z = -1 + -3i + 2iz + -5z + 1 + 3i + -2iz + 5z

Reorder the terms:
1 + Z2 + 3i + -2iz + 5z = -1 + 1 + -3i + 3i + 2iz + -2iz + -5z + 5z

Combine like terms: -1 + 1 = 0
1 + Z2 + 3i + -2iz + 5z = 0 + -3i + 3i + 2iz + -2iz + -5z + 5z
1 + Z2 + 3i + -2iz + 5z = -3i + 3i + 2iz + -2iz + -5z + 5z

Combine like terms: -3i + 3i = 0
1 + Z2 + 3i + -2iz + 5z = 0 + 2iz + -2iz + -5z + 5z
1 + Z2 + 3i + -2iz + 5z = 2iz + -2iz + -5z + 5z

Combine like terms: 2iz + -2iz = 0
1 + Z2 + 3i + -2iz + 5z = 0 + -5z + 5z
1 + Z2 + 3i + -2iz + 5z = -5z + 5z

Combine like terms: -5z + 5z = 0
1 + Z2 + 3i + -2iz + 5z = 0

The solution to this equation could not be determined.

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