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

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

Simplifying
z2 + -1(3 + -2i) * z + 1 = 0

Reorder the terms for easier multiplication:
z2 + -1z(3 + -2i) + 1 = 0
z2 + (3 * -1z + -2i * -1z) + 1 = 0

Reorder the terms:
z2 + (2iz + -3z) + 1 = 0
z2 + (2iz + -3z) + 1 = 0

Reorder the terms:
1 + 2iz + -3z + z2 = 0

Solving
1 + 2iz + -3z + z2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + 2iz + -3z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 2iz + -3z + z2 = 0 + -1

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

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

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

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

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

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

Divide each side by '2z'.
i = -0.5z-1 + 1.5 + -0.5z

Simplifying
i = -0.5z-1 + 1.5 + -0.5z

Reorder the terms:
i = 1.5 + -0.5z-1 + -0.5z