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Simplifying
(8 + 9i)(8 + -9i) = 0
Multiply (8 + 9i) * (8 + -9i)
(8(8 + -9i) + 9i * (8 + -9i)) = 0
((8 * 8 + -9i * 8) + 9i * (8 + -9i)) = 0
((64 + -72i) + 9i * (8 + -9i)) = 0
(64 + -72i + (8 * 9i + -9i * 9i)) = 0
(64 + -72i + (72i + -81i2)) = 0
Combine like terms: -72i + 72i = 0
(64 + 0 + -81i2) = 0
(64 + -81i2) = 0
Solving
64 + -81i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-64' to each side of the equation.
64 + -64 + -81i2 = 0 + -64
Combine like terms: 64 + -64 = 0
0 + -81i2 = 0 + -64
-81i2 = 0 + -64
Combine like terms: 0 + -64 = -64
-81i2 = -64
Divide each side by '-81'.
i2 = 0.7901234568
Simplifying
i2 = 0.7901234568
Take the square root of each side:
i = {-0.888888889, 0.888888889}
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