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

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


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

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

Multiply (3 + 2i) * (1 + 3i)
z2 + -1z(3(1 + 3i) + 2i * (1 + 3i)) = 0
z2 + -1z((1 * 3 + 3i * 3) + 2i * (1 + 3i)) = 0
z2 + -1z((3 + 9i) + 2i * (1 + 3i)) = 0
z2 + -1z(3 + 9i + (1 * 2i + 3i * 2i)) = 0
z2 + -1z(3 + 9i + (2i + 6i2)) = 0

Combine like terms: 9i + 2i = 11i
z2 + -1z(3 + 11i + 6i2) = 0
z2 + (3 * -1z + 11i * -1z + 6i2 * -1z) = 0

Reorder the terms:
z2 + (-11iz + -6i2z + -3z) = 0
z2 + (-11iz + -6i2z + -3z) = 0

Reorder the terms:
-11iz + -6i2z + -3z + z2 = 0

Solving
-11iz + -6i2z + -3z + z2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-11i + -6i2 + -3 + z) = 0


Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Add '-1z' to each side of the equation.
z + -1z = 0 + -1z
Remove the zero:
0 = -1z

Simplifying
0 = -1z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-11i + -6i2 + -3 + z)' equal to zero and attempt to solve:

Simplifying
-11i + -6i2 + -3 + z = 0

Reorder the terms:
-3 + -11i + -6i2 + z = 0

Solving
-3 + -11i + -6i2 + z = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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