(-4+2i)-(-6+5i)=(2+bi)

Solution for (-4+2i)-(-6+5i)=(2+bi) equation:

Simplifying
(-4 + 2i) + -1(-6 + 5i) = (2 + bi)

Remove parenthesis around (-4 + 2i)
-4 + 2i + -1(-6 + 5i) = (2 + bi)
-4 + 2i + (-6 * -1 + 5i * -1) = (2 + bi)
-4 + 2i + (6 + -5i) = (2 + bi)

Reorder the terms:
-4 + 6 + 2i + -5i = (2 + bi)

Combine like terms: -4 + 6 = 2
2 + 2i + -5i = (2 + bi)

Combine like terms: 2i + -5i = -3i
2 + -3i = (2 + bi)

Remove parenthesis around (2 + bi)
2 + -3i = 2 + bi

Add '-2' to each side of the equation.
2 + -2 + -3i = 2 + -2 + bi

Combine like terms: 2 + -2 = 0
0 + -3i = 2 + -2 + bi
-3i = 2 + -2 + bi

Combine like terms: 2 + -2 = 0
-3i = 0 + bi
-3i = bi

Solving
-3i = bi

Solving for variable 'i'.

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

Add '-1bi' to each side of the equation.
-1bi + -3i = bi + -1bi

Combine like terms: bi + -1bi = 0
-1bi + -3i = 0

Factor out the Greatest Common Factor (GCF), '-1i'.
-1i(b + 3) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0
Subproblem 2
Set the factor '(b + 3)' equal to zero and attempt to solve:

Simplifying
b + 3 = 0

Reorder the terms:
3 + b = 0

Solving
3 + b = 0

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

Add '-3' to each side of the equation.
3 + -3 + b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Add '-1b' to each side of the equation.
b + -1b = -3 + -1b

Combine like terms: b + -1b = 0
0 = -3 + -1b

Simplifying
0 = -3 + -1b

The solution to this equation could not be determined.

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