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

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

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

Reorder the terms for easier multiplication:
z2 + -1z(3 + 5i) + (3 + 5i) = 0
z2 + (3 * -1z + 5i * -1z) + (3 + 5i) = 0

Reorder the terms:
z2 + (-5iz + -3z) + (3 + 5i) = 0
z2 + (-5iz + -3z) + (3 + 5i) = 0

Remove parenthesis around (3 + 5i)
z2 + -5iz + -3z + 3 + 5i = 0

Reorder the terms:
3 + 5i + -5iz + -3z + z2 = 0

Solving
3 + 5i + -5iz + -3z + 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 + 5i + -5iz + -3z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 5i + -5iz + -3z + z2 = 0 + -3

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

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

Add '3z' to each side of the equation.
5i + -5iz + -3z + 3z + z2 = -3 + 3z

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

Add '-1z2' to each side of the equation.
5i + -5iz + z2 + -1z2 = -3 + 3z + -1z2

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

Reorder the terms:
3 + 5i + -5iz + -3z + z2 = -3 + 3z + -1z2 + 3 + -3z + z2

Reorder the terms:
3 + 5i + -5iz + -3z + z2 = -3 + 3 + 3z + -3z + -1z2 + z2

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

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

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

The solution to this equation could not be determined.