(j-3)(j-1)=0

Solution for (j-3)(j-1)=0 equation:

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

Reorder the terms:
(-3 + j)(j + -1) = 0

Reorder the terms:
(-3 + j)(-1 + j) = 0

Multiply (-3 + j) * (-1 + j)
(-3(-1 + j) + j(-1 + j)) = 0
((-1 * -3 + j * -3) + j(-1 + j)) = 0
((3 + -3j) + j(-1 + j)) = 0
(3 + -3j + (-1 * j + j * j)) = 0
(3 + -3j + (-1j + j2)) = 0

Combine like terms: -3j + -1j = -4j
(3 + -4j + j2) = 0

Solving
3 + -4j + j2 = 0

Solving for variable 'j'.

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

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

Simplifying
1 + -1j = 0

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

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

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

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

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