(3+10i)(4-9i)=

Solution for (3+10i)(4-9i)= equation:

Simplifying
(3 + 10i)(4 + -9i) = 0

Multiply (3 + 10i) * (4 + -9i)
(3(4 + -9i) + 10i * (4 + -9i)) = 0
((4 * 3 + -9i * 3) + 10i * (4 + -9i)) = 0
((12 + -27i) + 10i * (4 + -9i)) = 0
(12 + -27i + (4 * 10i + -9i * 10i)) = 0
(12 + -27i + (40i + -90i2)) = 0

Combine like terms: -27i + 40i = 13i
(12 + 13i + -90i2) = 0

Solving
12 + 13i + -90i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(4 + -9i)(3 + 10i) = 0

Subproblem 1
Set the factor '(4 + -9i)' equal to zero and attempt to solve:

Simplifying
4 + -9i = 0

Solving
4 + -9i = 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 + -9i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9i = 0 + -4
-9i = 0 + -4

Combine like terms: 0 + -4 = -4
-9i = -4

Divide each side by '-9'.
i = 0.4444444444

Simplifying
i = 0.4444444444
Subproblem 2
Set the factor '(3 + 10i)' equal to zero and attempt to solve:

Simplifying
3 + 10i = 0

Solving
3 + 10i = 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 + 10i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 10i = 0 + -3
10i = 0 + -3

Combine like terms: 0 + -3 = -3
10i = -3

Divide each side by '10'.
i = -0.3

Simplifying
i = -0.3
Solution
i = {0.4444444444, -0.3}