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

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

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

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

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

Combine like terms: 6 + -5 = 1
1 + -3i + 4i = 0

Combine like terms: -3i + 4i = 1i
1 + 1i = 0

Solving
1 + 1i = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -1 + 1i = 0 + -1

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

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

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

Simplifying
i = -1