(8+2i)(4+4i)=

Solution for (8+2i)(4+4i)= equation:

Simplifying
(8 + 2i)(4 + 4i) = 0

Multiply (8 + 2i) * (4 + 4i)
(8(4 + 4i) + 2i * (4 + 4i)) = 0
((4 * 8 + 4i * 8) + 2i * (4 + 4i)) = 0
((32 + 32i) + 2i * (4 + 4i)) = 0
(32 + 32i + (4 * 2i + 4i * 2i)) = 0
(32 + 32i + (8i + 8i2)) = 0

Combine like terms: 32i + 8i = 40i
(32 + 40i + 8i2) = 0

Solving
32 + 40i + 8i2 = 0

Solving for variable 'i'.

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

Factor a trinomial.
8((4 + i)(1 + i)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve:

Simplifying
4 + i = 0

Solving
4 + i = 0

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

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

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

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

Simplifying
i = -4
Subproblem 2
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
Solution
i = {-4, -1}