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Simplifying
(3i + -8)(3i + 8) = 0
Reorder the terms:
(-8 + 3i)(3i + 8) = 0
Reorder the terms:
(-8 + 3i)(8 + 3i) = 0
Multiply (-8 + 3i) * (8 + 3i)
(-8(8 + 3i) + 3i * (8 + 3i)) = 0
((8 * -8 + 3i * -8) + 3i * (8 + 3i)) = 0
((-64 + -24i) + 3i * (8 + 3i)) = 0
(-64 + -24i + (8 * 3i + 3i * 3i)) = 0
(-64 + -24i + (24i + 9i2)) = 0
Combine like terms: -24i + 24i = 0
(-64 + 0 + 9i2) = 0
(-64 + 9i2) = 0
Solving
-64 + 9i2 = 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 + 9i2 = 0 + 64
Combine like terms: -64 + 64 = 0
0 + 9i2 = 0 + 64
9i2 = 0 + 64
Combine like terms: 0 + 64 = 64
9i2 = 64
Divide each side by '9'.
i2 = 7.111111111
Simplifying
i2 = 7.111111111
Take the square root of each side:
i = {-2.666666667, 2.666666667}
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