(1+j)(6-2j)=

Solution for (1+j)(6-2j)= equation:

Simplifying
(1 + j)(6 + -2j) = 0

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

Combine like terms: -2j + 6j = 4j
(6 + 4j + -2j2) = 0

Solving
6 + 4j + -2j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2j + -1j2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1j)' equal to zero and attempt to solve:

Simplifying
3 + -1j = 0

Solving
3 + -1j = 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 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Subproblem 2
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
Solution
j = {3, -1}