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Simplifying
(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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