(4+6j)*(2+2j)=

Solution for (4+6j)*(2+2j)= equation:

Simplifying
(4 + 6j)(2 + 2j) = 0

Multiply (4 + 6j) * (2 + 2j)
(4(2 + 2j) + 6j * (2 + 2j)) = 0
((2 * 4 + 2j * 4) + 6j * (2 + 2j)) = 0
((8 + 8j) + 6j * (2 + 2j)) = 0
(8 + 8j + (2 * 6j + 2j * 6j)) = 0
(8 + 8j + (12j + 12j2)) = 0

Combine like terms: 8j + 12j = 20j
(8 + 20j + 12j2) = 0

Solving
8 + 20j + 12j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 5j + 3j2) = 0

Factor a trinomial.
4((1 + j)(2 + 3j)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + j)' equal to zero and attempt to solve:

Simplifying
1 + j = 0

Solving
1 + j = 0

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

Add '-1' to each side of the equation.
1 + -1 + j = 0 + -1

Combine like terms: 1 + -1 = 0
0 + j = 0 + -1
j = 0 + -1

Combine like terms: 0 + -1 = -1
j = -1

Simplifying
j = -1
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 = {-1, -0.6666666667}