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Simplifying
(x + -3i)(x + 3i) * x = 0
Reorder the terms:
(-3i + x)(x + 3i) * x = 0
Reorder the terms:
(-3i + x)(3i + x) * x = 0
Reorder the terms for easier multiplication:
x(-3i + x)(3i + x) = 0
Multiply (-3i + x) * (3i + x)
x(-3i * (3i + x) + x(3i + x)) = 0
x((3i * -3i + x * -3i) + x(3i + x)) = 0
Reorder the terms:
x((-3ix + -9i2) + x(3i + x)) = 0
x((-3ix + -9i2) + x(3i + x)) = 0
x(-3ix + -9i2 + (3i * x + x * x)) = 0
x(-3ix + -9i2 + (3ix + x2)) = 0
Reorder the terms:
x(-3ix + 3ix + -9i2 + x2) = 0
Combine like terms: -3ix + 3ix = 0
x(0 + -9i2 + x2) = 0
x(-9i2 + x2) = 0
(-9i2 * x + x2 * x) = 0
(-9i2x + x3) = 0
Solving
-9i2x + x3 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-1x3' to each side of the equation.
-9i2x + x3 + -1x3 = 0 + -1x3
Combine like terms: x3 + -1x3 = 0
-9i2x + 0 = 0 + -1x3
-9i2x = 0 + -1x3
Remove the zero:
-9i2x = -1x3
Divide each side by '-9x'.
i2 = 0.1111111111x2
Simplifying
i2 = 0.1111111111x2
Take the square root of each side:
i = {-0.333333333x, 0.333333333x}
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