(6-3i)-(4-5i)=0

Solution for (6-3i)-(4-5i)=0 equation:

Simplifying
(6 + -3i) + -1(4 + -5i) = 0

Remove parenthesis around (6 + -3i)
6 + -3i + -1(4 + -5i) = 0
6 + -3i + (4 * -1 + -5i * -1) = 0
6 + -3i + (-4 + 5i) = 0

Reorder the terms:
6 + -4 + -3i + 5i = 0

Combine like terms: 6 + -4 = 2
2 + -3i + 5i = 0

Combine like terms: -3i + 5i = 2i
2 + 2i = 0

Solving
2 + 2i = 0

Solving for variable 'i'.

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

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

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

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

Divide each side by '2'.
i = -1

Simplifying
i = -1