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

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

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

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

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

Reorder the terms:
-5 + 6 + -1i + 2i = 0

Combine like terms: -5 + 6 = 1
1 + -1i + 2i = 0

Combine like terms: -1i + 2i = 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