(3+5i)(4+4i)=0

Solution for (3+5i)(4+4i)=0 equation:

Simplifying
(3 + 5i)(4 + 4i) = 0

Multiply (3 + 5i) * (4 + 4i)
(3(4 + 4i) + 5i * (4 + 4i)) = 0
((4 * 3 + 4i * 3) + 5i * (4 + 4i)) = 0
((12 + 12i) + 5i * (4 + 4i)) = 0
(12 + 12i + (4 * 5i + 4i * 5i)) = 0
(12 + 12i + (20i + 20i2)) = 0

Combine like terms: 12i + 20i = 32i
(12 + 32i + 20i2) = 0

Solving
12 + 32i + 20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 8i + 5i2) = 0

Factor a trinomial.
4((1 + i)(3 + 5i)) = 0

Ignore the factor 4.
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 + 5i)' equal to zero and attempt to solve:

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

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

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

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {-1, -0.6}