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Simplifying
(8 + 4i)(8 + -4i) = 0
Multiply (8 + 4i) * (8 + -4i)
(8(8 + -4i) + 4i * (8 + -4i)) = 0
((8 * 8 + -4i * 8) + 4i * (8 + -4i)) = 0
((64 + -32i) + 4i * (8 + -4i)) = 0
(64 + -32i + (8 * 4i + -4i * 4i)) = 0
(64 + -32i + (32i + -16i2)) = 0
Combine like terms: -32i + 32i = 0
(64 + 0 + -16i2) = 0
(64 + -16i2) = 0
Solving
64 + -16i2 = 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 + -16i2 = 0 + -64
Combine like terms: 64 + -64 = 0
0 + -16i2 = 0 + -64
-16i2 = 0 + -64
Combine like terms: 0 + -64 = -64
-16i2 = -64
Divide each side by '-16'.
i2 = 4
Simplifying
i2 = 4
Take the square root of each side:
i = {-2, 2}
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