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Simplifying
(4 + -3i)(8 + 6i) = 0
Multiply (4 + -3i) * (8 + 6i)
(4(8 + 6i) + -3i * (8 + 6i)) = 0
((8 * 4 + 6i * 4) + -3i * (8 + 6i)) = 0
((32 + 24i) + -3i * (8 + 6i)) = 0
(32 + 24i + (8 * -3i + 6i * -3i)) = 0
(32 + 24i + (-24i + -18i2)) = 0
Combine like terms: 24i + -24i = 0
(32 + 0 + -18i2) = 0
(32 + -18i2) = 0
Solving
32 + -18i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-32' to each side of the equation.
32 + -32 + -18i2 = 0 + -32
Combine like terms: 32 + -32 = 0
0 + -18i2 = 0 + -32
-18i2 = 0 + -32
Combine like terms: 0 + -32 = -32
-18i2 = -32
Divide each side by '-18'.
i2 = 1.777777778
Simplifying
i2 = 1.777777778
Take the square root of each side:
i = {-1.333333333, 1.333333333}
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