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

Solution for (3+4i)-(1-5i)=0 equation:

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

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

Reorder the terms:
3 + -1 + 4i + 5i = 0

Combine like terms: 3 + -1 = 2
2 + 4i + 5i = 0

Combine like terms: 4i + 5i = 9i
2 + 9i = 0

Solving
2 + 9i = 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 + 9i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9i = 0 + -2
9i = 0 + -2

Combine like terms: 0 + -2 = -2
9i = -2

Divide each side by '9'.
i = -0.2222222222

Simplifying
i = -0.2222222222