(3+4i)(4-8i)=

Solution for (3+4i)(4-8i)= equation:

Simplifying
(3 + 4i)(4 + -8i) = 0

Multiply (3 + 4i) * (4 + -8i)
(3(4 + -8i) + 4i * (4 + -8i)) = 0
((4 * 3 + -8i * 3) + 4i * (4 + -8i)) = 0
((12 + -24i) + 4i * (4 + -8i)) = 0
(12 + -24i + (4 * 4i + -8i * 4i)) = 0
(12 + -24i + (16i + -32i2)) = 0

Combine like terms: -24i + 16i = -8i
(12 + -8i + -32i2) = 0

Solving
12 + -8i + -32i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -2i + -8i2) = 0

Factor a trinomial.
4((1 + -2i)(3 + 4i)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
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 = {0.5, -0.75}