(4+18i)(6-8i)=

Solution for (4+18i)(6-8i)= equation:

Simplifying
(4 + 18i)(6 + -8i) = 0

Multiply (4 + 18i) * (6 + -8i)
(4(6 + -8i) + 18i * (6 + -8i)) = 0
((6 * 4 + -8i * 4) + 18i * (6 + -8i)) = 0
((24 + -32i) + 18i * (6 + -8i)) = 0
(24 + -32i + (6 * 18i + -8i * 18i)) = 0
(24 + -32i + (108i + -144i2)) = 0

Combine like terms: -32i + 108i = 76i
(24 + 76i + -144i2) = 0

Solving
24 + 76i + -144i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 19i + -36i2) = 0

Factor a trinomial.
4((3 + -4i)(2 + 9i)) = 0

Ignore the factor 4.
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 '(2 + 9i)' equal to zero and attempt to solve:

Simplifying
2 + 9i = 0

Solving
2 + 9i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 9i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9i = 0 + -2
9i = 0 + -2

Combine like terms: 0 + -2 = -2
9i = -2

Divide each side by '9'.
i = -0.2222222222

Simplifying
i = -0.2222222222
Solution
i = {0.75, -0.2222222222}