z^2-5+i+8+i=0

Solution for z^2-5+i+8+i=0 equation:

Simplifying
z2 + -5 + i + 8 + i = 0

Reorder the terms:
-5 + 8 + i + i + z2 = 0

Combine like terms: -5 + 8 = 3
3 + i + i + z2 = 0

Combine like terms: i + i = 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