z^2-(1+2i)*z+2i=0

Solution for z^2-(1+2i)*z+2i=0 equation:

Simplifying
z2 + -1(1 + 2i) * z + 2i = 0

Reorder the terms for easier multiplication:
z2 + -1z(1 + 2i) + 2i = 0
z2 + (1 * -1z + 2i * -1z) + 2i = 0

Reorder the terms:
z2 + (-2iz + -1z) + 2i = 0
z2 + (-2iz + -1z) + 2i = 0

Reorder the terms:
2i + -2iz + -1z + z2 = 0

Solving
2i + -2iz + -1z + z2 = 0

Solving for variable 'i'.

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

Add 'z' to each side of the equation.
2i + -2iz + -1z + z + z2 = 0 + z

Combine like terms: -1z + z = 0
2i + -2iz + 0 + z2 = 0 + z
2i + -2iz + z2 = 0 + z
Remove the zero:
2i + -2iz + z2 = z

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

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

Reorder the terms:
2i + -2iz + -1z + z2 = z + -1z + -1z2 + z2

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

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

The solution to this equation could not be determined.