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