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

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

Simplifying
(3 + 4i)(3 + -4i) + (3 + 4i) = 0

Multiply (3 + 4i) * (3 + -4i)
(3(3 + -4i) + 4i * (3 + -4i)) + (3 + 4i) = 0
((3 * 3 + -4i * 3) + 4i * (3 + -4i)) + (3 + 4i) = 0
((9 + -12i) + 4i * (3 + -4i)) + (3 + 4i) = 0
(9 + -12i + (3 * 4i + -4i * 4i)) + (3 + 4i) = 0
(9 + -12i + (12i + -16i2)) + (3 + 4i) = 0

Combine like terms: -12i + 12i = 0
(9 + 0 + -16i2) + (3 + 4i) = 0
(9 + -16i2) + (3 + 4i) = 0

Remove parenthesis around (3 + 4i)
9 + -16i2 + 3 + 4i = 0

Reorder the terms:
9 + 3 + 4i + -16i2 = 0

Combine like terms: 9 + 3 = 12
12 + 4i + -16i2 = 0

Solving
12 + 4i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + i + -4i2) = 0

Factor a trinomial.
4((1 + -1i)(3 + 4i)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

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
Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {1, -0.75}