(0.5+0.5j)*(0.5-0.5j)=0

Solution for (0.5+0.5j)*(0.5-0.5j)=0 equation:

Simplifying
(0.5 + 0.5j)(0.5 + -0.5j) = 0

Multiply (0.5 + 0.5j) * (0.5 + -0.5j)
(0.5(0.5 + -0.5j) + 0.5j * (0.5 + -0.5j)) = 0
((0.5 * 0.5 + -0.5j * 0.5) + 0.5j * (0.5 + -0.5j)) = 0
((0.25 + -0.25j) + 0.5j * (0.5 + -0.5j)) = 0
(0.25 + -0.25j + (0.5 * 0.5j + -0.5j * 0.5j)) = 0
(0.25 + -0.25j + (0.25j + -0.25j2)) = 0

Combine like terms: -0.25j + 0.25j = 0.00
(0.25 + 0.00 + -0.25j2) = 0
(0.25 + -0.25j2) = 0

Solving
0.25 + -0.25j2 = 0

Solving for variable 'j'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + -0.25j2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.25j2 = 0 + -0.25
-0.25j2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.25j2 = -0.25

Divide each side by '-0.25'.
j2 = 1

Simplifying
j2 = 1

Take the square root of each side:
j = {-1, 1}