(5+5i)(3-3i)=0

Solution for (5+5i)(3-3i)=0 equation:

Simplifying
(5 + 5i)(3 + -3i) = 0

Multiply (5 + 5i) * (3 + -3i)
(5(3 + -3i) + 5i * (3 + -3i)) = 0
((3 * 5 + -3i * 5) + 5i * (3 + -3i)) = 0
((15 + -15i) + 5i * (3 + -3i)) = 0
(15 + -15i + (3 * 5i + -3i * 5i)) = 0
(15 + -15i + (15i + -15i2)) = 0

Combine like terms: -15i + 15i = 0
(15 + 0 + -15i2) = 0
(15 + -15i2) = 0

Solving
15 + -15i2 = 0

Solving for variable 'i'.

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

Add '-15' to each side of the equation.
15 + -15 + -15i2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -15i2 = 0 + -15
-15i2 = 0 + -15

Combine like terms: 0 + -15 = -15
-15i2 = -15

Divide each side by '-15'.
i2 = 1

Simplifying
i2 = 1

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