(5+9i)(3+i)=

Solution for (5+9i)(3+i)= equation:

Simplifying
(5 + 9i)(3 + i) = 0

Multiply (5 + 9i) * (3 + i)
(5(3 + i) + 9i * (3 + i)) = 0
((3 * 5 + i * 5) + 9i * (3 + i)) = 0
((15 + 5i) + 9i * (3 + i)) = 0
(15 + 5i + (3 * 9i + i * 9i)) = 0
(15 + 5i + (27i + 9i2)) = 0

Combine like terms: 5i + 27i = 32i
(15 + 32i + 9i2) = 0

Solving
15 + 32i + 9i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + i)(5 + 9i) = 0

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

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Subproblem 2
Set the factor '(5 + 9i)' equal to zero and attempt to solve:

Simplifying
5 + 9i = 0

Solving
5 + 9i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 9i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9i = 0 + -5
9i = 0 + -5

Combine like terms: 0 + -5 = -5
9i = -5

Divide each side by '9'.
i = -0.5555555556

Simplifying
i = -0.5555555556
Solution
i = {-3, -0.5555555556}