F(z)=(2+2i)z

Solution for F(z)=(2+2i)z equation:

Simplifying
F(z) = (2 + 2i) * z

Multiply F * z
zF = (2 + 2i) * z

Reorder the terms for easier multiplication:
zF = z(2 + 2i)
zF = (2 * z + 2i * z)

Reorder the terms:
zF = (2iz + 2z)
zF = (2iz + 2z)

Solving
zF = 2iz + 2z

Solving for variable 'z'.

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

Add '-2iz' to each side of the equation.
-2iz + zF = 2iz + -2iz + 2z

Combine like terms: 2iz + -2iz = 0
-2iz + zF = 0 + 2z
-2iz + zF = 2z

Add '-2z' to each side of the equation.
-2iz + -2z + zF = 2z + -2z

Combine like terms: 2z + -2z = 0
-2iz + -2z + zF = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-2i + -2 + F) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-2i + -2 + F)' equal to zero and attempt to solve:

Simplifying
-2i + -2 + F = 0

Reorder the terms:
-2 + F + -2i = 0

Solving
-2 + F + -2i = 0

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

Add '2' to each side of the equation.
-2 + F + 2 + -2i = 0 + 2

Reorder the terms:
-2 + 2 + F + -2i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + F + -2i = 0 + 2
F + -2i = 0 + 2

Combine like terms: 0 + 2 = 2
F + -2i = 2

Add '-1F' to each side of the equation.
F + -1F + -2i = 2 + -1F

Combine like terms: F + -1F = 0
0 + -2i = 2 + -1F
-2i = 2 + -1F

Add '2i' to each side of the equation.
-2i + 2i = 2 + -1F + 2i

Combine like terms: -2i + 2i = 0
0 = 2 + -1F + 2i

Simplifying
0 = 2 + -1F + 2i

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}