(3+4i)(1+i)=0

Solution for (3+4i)(1+i)=0 equation:

Simplifying
(3 + 4i)(1 + i) = 0

Multiply (3 + 4i) * (1 + i)
(3(1 + i) + 4i * (1 + i)) = 0
((1 * 3 + i * 3) + 4i * (1 + i)) = 0
((3 + 3i) + 4i * (1 + i)) = 0
(3 + 3i + (1 * 4i + i * 4i)) = 0
(3 + 3i + (4i + 4i2)) = 0

Combine like terms: 3i + 4i = 7i
(3 + 7i + 4i2) = 0

Solving
3 + 7i + 4i2 = 0

Solving for variable 'i'.

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

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

Simplifying
1 + i = 0

Solving
1 + i = 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 + i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + i = 0 + -1
i = 0 + -1

Combine like terms: 0 + -1 = -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}