(3-i)-(2+6i)=

Solution for (3-i)-(2+6i)= equation:

Simplifying
(3 + -1i) + -1(2 + 6i) = 0

Remove parenthesis around (3 + -1i)
3 + -1i + -1(2 + 6i) = 0
3 + -1i + (2 * -1 + 6i * -1) = 0
3 + -1i + (-2 + -6i) = 0

Reorder the terms:
3 + -2 + -1i + -6i = 0

Combine like terms: 3 + -2 = 1
1 + -1i + -6i = 0

Combine like terms: -1i + -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