(3+i)-(4-6i)=

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

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

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

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

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

Combine like terms: i + 6i = 7i
-1 + 7i = 0

Solving
-1 + 7i = 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 + 7i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7i = 0 + 1
7i = 0 + 1

Combine like terms: 0 + 1 = 1
7i = 1

Divide each side by '7'.
i = 0.1428571429

Simplifying
i = 0.1428571429