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Simplifying
(9 + 9i)(20 + -20i) = 0
Multiply (9 + 9i) * (20 + -20i)
(9(20 + -20i) + 9i * (20 + -20i)) = 0
((20 * 9 + -20i * 9) + 9i * (20 + -20i)) = 0
((180 + -180i) + 9i * (20 + -20i)) = 0
(180 + -180i + (20 * 9i + -20i * 9i)) = 0
(180 + -180i + (180i + -180i2)) = 0
Combine like terms: -180i + 180i = 0
(180 + 0 + -180i2) = 0
(180 + -180i2) = 0
Solving
180 + -180i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-180' to each side of the equation.
180 + -180 + -180i2 = 0 + -180
Combine like terms: 180 + -180 = 0
0 + -180i2 = 0 + -180
-180i2 = 0 + -180
Combine like terms: 0 + -180 = -180
-180i2 = -180
Divide each side by '-180'.
i2 = 1
Simplifying
i2 = 1
Take the square root of each side:
i = {-1, 1}
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