(3+4i)+(3-4i)=a+bi

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

Simplifying
(3 + 4i) + (3 + -4i) = a + bi

Remove parenthesis around (3 + 4i)
3 + 4i + (3 + -4i) = a + bi

Remove parenthesis around (3 + -4i)
3 + 4i + 3 + -4i = a + bi

Reorder the terms:
3 + 3 + 4i + -4i = a + bi

Combine like terms: 3 + 3 = 6
6 + 4i + -4i = a + bi

Combine like terms: 4i + -4i = 0
6 + 0 = a + bi
6 = a + bi

Solving
6 = a + bi

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
6 + -1a = a + -1a + bi

Combine like terms: a + -1a = 0
6 + -1a = 0 + bi
6 + -1a = bi

Add '-6' to each side of the equation.
6 + -6 + -1a = -6 + bi

Combine like terms: 6 + -6 = 0
0 + -1a = -6 + bi
-1a = -6 + bi

Divide each side by '-1'.
a = 6 + -1bi

Simplifying
a = 6 + -1bi