(5+9i)(5-9i)=0

Solution for (5+9i)(5-9i)=0 equation:

Simplifying
(5 + 9i)(5 + -9i) = 0

Multiply (5 + 9i) * (5 + -9i)
(5(5 + -9i) + 9i * (5 + -9i)) = 0
((5 * 5 + -9i * 5) + 9i * (5 + -9i)) = 0
((25 + -45i) + 9i * (5 + -9i)) = 0
(25 + -45i + (5 * 9i + -9i * 9i)) = 0
(25 + -45i + (45i + -81i2)) = 0

Combine like terms: -45i + 45i = 0
(25 + 0 + -81i2) = 0
(25 + -81i2) = 0

Solving
25 + -81i2 = 0

Solving for variable 'i'.

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

Add '-25' to each side of the equation.
25 + -25 + -81i2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -81i2 = 0 + -25
-81i2 = 0 + -25

Combine like terms: 0 + -25 = -25
-81i2 = -25

Divide each side by '-81'.
i2 = 0.3086419753

Simplifying
i2 = 0.3086419753

Take the square root of each side:
i = {-0.555555556, 0.555555556}