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

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

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

Multiply (3 + -4i) * (3 + 8i)
(3(3 + 8i) + -4i * (3 + 8i)) = 0
((3 * 3 + 8i * 3) + -4i * (3 + 8i)) = 0
((9 + 24i) + -4i * (3 + 8i)) = 0
(9 + 24i + (3 * -4i + 8i * -4i)) = 0
(9 + 24i + (-12i + -32i2)) = 0

Combine like terms: 24i + -12i = 12i
(9 + 12i + -32i2) = 0

Solving
9 + 12i + -32i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -4i)(3 + 8i) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 8i)' equal to zero and attempt to solve:

Simplifying
3 + 8i = 0

Solving
3 + 8i = 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 + 8i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8i = 0 + -3
8i = 0 + -3

Combine like terms: 0 + -3 = -3
8i = -3

Divide each side by '8'.
i = -0.375

Simplifying
i = -0.375
Solution
i = {0.75, -0.375}