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Simplifying
(4 + 3i)(3i + -4) = 0
Reorder the terms:
(4 + 3i)(-4 + 3i) = 0
Multiply (4 + 3i) * (-4 + 3i)
(4(-4 + 3i) + 3i * (-4 + 3i)) = 0
((-4 * 4 + 3i * 4) + 3i * (-4 + 3i)) = 0
((-16 + 12i) + 3i * (-4 + 3i)) = 0
(-16 + 12i + (-4 * 3i + 3i * 3i)) = 0
(-16 + 12i + (-12i + 9i2)) = 0
Combine like terms: 12i + -12i = 0
(-16 + 0 + 9i2) = 0
(-16 + 9i2) = 0
Solving
-16 + 9i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '16' to each side of the equation.
-16 + 16 + 9i2 = 0 + 16
Combine like terms: -16 + 16 = 0
0 + 9i2 = 0 + 16
9i2 = 0 + 16
Combine like terms: 0 + 16 = 16
9i2 = 16
Divide each side by '9'.
i2 = 1.777777778
Simplifying
i2 = 1.777777778
Take the square root of each side:
i = {-1.333333333, 1.333333333}
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