(3-9i)+(3+7i)=0

Solution for (3-9i)+(3+7i)=0 equation:

Simplifying
(3 + -9i) + (3 + 7i) = 0

Remove parenthesis around (3 + -9i)
3 + -9i + (3 + 7i) = 0

Remove parenthesis around (3 + 7i)
3 + -9i + 3 + 7i = 0

Reorder the terms:
3 + 3 + -9i + 7i = 0

Combine like terms: 3 + 3 = 6
6 + -9i + 7i = 0

Combine like terms: -9i + 7i = -2i
6 + -2i = 0

Solving
6 + -2i = 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 + -2i = 0 + -6

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

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

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

Simplifying
i = 3