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Simplifying
(8 + -1i)(8 + i) = 0
Multiply (8 + -1i) * (8 + i)
(8(8 + i) + -1i * (8 + i)) = 0
((8 * 8 + i * 8) + -1i * (8 + i)) = 0
((64 + 8i) + -1i * (8 + i)) = 0
(64 + 8i + (8 * -1i + i * -1i)) = 0
(64 + 8i + (-8i + -1i2)) = 0
Combine like terms: 8i + -8i = 0
(64 + 0 + -1i2) = 0
(64 + -1i2) = 0
Solving
64 + -1i2 = 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 + -1i2 = 0 + -64
Combine like terms: 64 + -64 = 0
0 + -1i2 = 0 + -64
-1i2 = 0 + -64
Combine like terms: 0 + -64 = -64
-1i2 = -64
Divide each side by '-1'.
i2 = 64
Simplifying
i2 = 64
Take the square root of each side:
i = {-8, 8}
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