(5-2i)+(1+5i)=

Solution for (5-2i)+(1+5i)= equation:

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

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

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

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

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

Combine like terms: -2i + 5i = 3i
6 + 3i = 0

Solving
6 + 3i = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + 3i = 0 + -6

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

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

Divide each side by '3'.
i = -2

Simplifying
i = -2