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Simplifying
(9 + 3i)(9 + -3i) = 0
Multiply (9 + 3i) * (9 + -3i)
(9(9 + -3i) + 3i * (9 + -3i)) = 0
((9 * 9 + -3i * 9) + 3i * (9 + -3i)) = 0
((81 + -27i) + 3i * (9 + -3i)) = 0
(81 + -27i + (9 * 3i + -3i * 3i)) = 0
(81 + -27i + (27i + -9i2)) = 0
Combine like terms: -27i + 27i = 0
(81 + 0 + -9i2) = 0
(81 + -9i2) = 0
Solving
81 + -9i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-81' to each side of the equation.
81 + -81 + -9i2 = 0 + -81
Combine like terms: 81 + -81 = 0
0 + -9i2 = 0 + -81
-9i2 = 0 + -81
Combine like terms: 0 + -81 = -81
-9i2 = -81
Divide each side by '-9'.
i2 = 9
Simplifying
i2 = 9
Take the square root of each side:
i = {-3, 3}
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