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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}
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