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

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

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

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

Combine like terms: 1j + -3j = -2j
(-3 + -2j + j2) = 0

Solving
-3 + -2j + 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}