(4+5i)-(6-2i)=0

Solution for (4+5i)-(6-2i)=0 equation:

Simplifying
(4 + 5i) + -1(6 + -2i) = 0

Remove parenthesis around (4 + 5i)
4 + 5i + -1(6 + -2i) = 0
4 + 5i + (6 * -1 + -2i * -1) = 0
4 + 5i + (-6 + 2i) = 0

Reorder the terms:
4 + -6 + 5i + 2i = 0

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

Combine like terms: 5i + 2i = 7i
-2 + 7i = 0

Solving
-2 + 7i = 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 + 7i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7i = 0 + 2
7i = 0 + 2

Combine like terms: 0 + 2 = 2
7i = 2

Divide each side by '7'.
i = 0.2857142857

Simplifying
i = 0.2857142857