=(2+3j)*(3+1j)

Solution for =(2+3j)*(3+1j) equation:

Simplifying
0 = (2 + 3j)(3 + 1j)

Multiply (2 + 3j) * (3 + 1j)
0 = (2(3 + 1j) + 3j * (3 + 1j))
0 = ((3 * 2 + 1j * 2) + 3j * (3 + 1j))
0 = ((6 + 2j) + 3j * (3 + 1j))
0 = (6 + 2j + (3 * 3j + 1j * 3j))
0 = (6 + 2j + (9j + 3j2))

Combine like terms: 2j + 9j = 11j
0 = (6 + 11j + 3j2)

Solving
0 = 6 + 11j + 3j2

Solving for variable 'j'.

Combine like terms: 0 + -6 = -6
-6 + -11j + -3j2 = 6 + 11j + 3j2 + -6 + -11j + -3j2

Reorder the terms:
-6 + -11j + -3j2 = 6 + -6 + 11j + -11j + 3j2 + -3j2

Combine like terms: 6 + -6 = 0
-6 + -11j + -3j2 = 0 + 11j + -11j + 3j2 + -3j2
-6 + -11j + -3j2 = 11j + -11j + 3j2 + -3j2

Combine like terms: 11j + -11j = 0
-6 + -11j + -3j2 = 0 + 3j2 + -3j2
-6 + -11j + -3j2 = 3j2 + -3j2

Combine like terms: 3j2 + -3j2 = 0
-6 + -11j + -3j2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11j + 3j2) = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + j)' equal to zero and attempt to solve:

Simplifying
3 + j = 0

Solving
3 + j = 0

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

Add '-3' to each side of the equation.
3 + -3 + j = 0 + -3

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

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

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

Simplifying
2 + 3j = 0

Solving
2 + 3j = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3j = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3j = 0 + -2
3j = 0 + -2

Combine like terms: 0 + -2 = -2
3j = -2

Divide each side by '3'.
j = -0.6666666667

Simplifying
j = -0.6666666667
Solution
j = {-3, -0.6666666667}