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Simplifying
(7 + -8i)(7 + 8i) = 0
Multiply (7 + -8i) * (7 + 8i)
(7(7 + 8i) + -8i * (7 + 8i)) = 0
((7 * 7 + 8i * 7) + -8i * (7 + 8i)) = 0
((49 + 56i) + -8i * (7 + 8i)) = 0
(49 + 56i + (7 * -8i + 8i * -8i)) = 0
(49 + 56i + (-56i + -64i2)) = 0
Combine like terms: 56i + -56i = 0
(49 + 0 + -64i2) = 0
(49 + -64i2) = 0
Solving
49 + -64i2 = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-49' to each side of the equation.
49 + -49 + -64i2 = 0 + -49
Combine like terms: 49 + -49 = 0
0 + -64i2 = 0 + -49
-64i2 = 0 + -49
Combine like terms: 0 + -49 = -49
-64i2 = -49
Divide each side by '-64'.
i2 = 0.765625
Simplifying
i2 = 0.765625
Take the square root of each side:
i = {-0.875, 0.875}
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