(-1.5+3j)*(1.5+3j)=

Solution for (-1.5+3j)*(1.5+3j)= equation:

Simplifying
(-1.5 + 3j)(1.5 + 3j) = 0

Multiply (-1.5 + 3j) * (1.5 + 3j)
(-1.5(1.5 + 3j) + 3j * (1.5 + 3j)) = 0
((1.5 * -1.5 + 3j * -1.5) + 3j * (1.5 + 3j)) = 0
((-2.25 + -4.5j) + 3j * (1.5 + 3j)) = 0
(-2.25 + -4.5j + (1.5 * 3j + 3j * 3j)) = 0
(-2.25 + -4.5j + (4.5j + 9j2)) = 0

Combine like terms: -4.5j + 4.5j = 0.0
(-2.25 + 0.0 + 9j2) = 0
(-2.25 + 9j2) = 0

Solving
-2.25 + 9j2 = 0

Solving for variable 'j'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + 9j2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 9j2 = 0 + 2.25
9j2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
9j2 = 2.25

Divide each side by '9'.
j2 = 0.25

Simplifying
j2 = 0.25

Take the square root of each side:
j = {-0.5, 0.5}