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Simplifying
(7 + i)(7 + -1i) = 0
Multiply (7 + i) * (7 + -1i)
(7(7 + -1i) + i(7 + -1i)) = 0
((7 * 7 + -1i * 7) + i(7 + -1i)) = 0
((49 + -7i) + i(7 + -1i)) = 0
(49 + -7i + (7 * i + -1i * i)) = 0
(49 + -7i + (7i + -1i2)) = 0
Combine like terms: -7i + 7i = 0
(49 + 0 + -1i2) = 0
(49 + -1i2) = 0
Solving
49 + -1i2 = 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 + -1i2 = 0 + -49
Combine like terms: 49 + -49 = 0
0 + -1i2 = 0 + -49
-1i2 = 0 + -49
Combine like terms: 0 + -49 = -49
-1i2 = -49
Divide each side by '-1'.
i2 = 49
Simplifying
i2 = 49
Take the square root of each side:
i = {-7, 7}
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