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

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

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

Multiply (3 + 5i) * (3 + -5i)
(3(3 + -5i) + 5i * (3 + -5i)) = 0
((3 * 3 + -5i * 3) + 5i * (3 + -5i)) = 0
((9 + -15i) + 5i * (3 + -5i)) = 0
(9 + -15i + (3 * 5i + -5i * 5i)) = 0
(9 + -15i + (15i + -25i2)) = 0

Combine like terms: -15i + 15i = 0
(9 + 0 + -25i2) = 0
(9 + -25i2) = 0

Solving
9 + -25i2 = 0

Solving for variable 'i'.

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

Add '-9' to each side of the equation.
9 + -9 + -25i2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -25i2 = 0 + -9
-25i2 = 0 + -9

Combine like terms: 0 + -9 = -9
-25i2 = -9

Divide each side by '-25'.
i2 = 0.36

Simplifying
i2 = 0.36

Take the square root of each side:
i = {-0.6, 0.6}