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

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

Simplifying
z2 + -1(4 + 3i) + 1 + 5i = 0
z2 + (4 * -1 + 3i * -1) + 1 + 5i = 0
z2 + (-4 + -3i) + 1 + 5i = 0

Reorder the terms:
-4 + 1 + -3i + 5i + z2 = 0

Combine like terms: -4 + 1 = -3
-3 + -3i + 5i + z2 = 0

Combine like terms: -3i + 5i = 2i
-3 + 2i + z2 = 0

Solving
-3 + 2i + z2 = 0

Solving for variable 'i'.

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

Add '3' to each side of the equation.
-3 + 2i + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 2i + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2i + z2 = 0 + 3
2i + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
2i + z2 = 3

Add '-1z2' to each side of the equation.
2i + z2 + -1z2 = 3 + -1z2

Combine like terms: z2 + -1z2 = 0
2i + 0 = 3 + -1z2
2i = 3 + -1z2

Divide each side by '2'.
i = 1.5 + -0.5z2

Simplifying
i = 1.5 + -0.5z2