(-7-i)(-7+i)=0

Solution for (-7-i)(-7+i)=0 equation:

Simplifying
(-7 + -1i)(-7 + i) = 0

Multiply (-7 + -1i) * (-7 + i)
(-7(-7 + i) + -1i * (-7 + i)) = 0
((-7 * -7 + i * -7) + -1i * (-7 + i)) = 0
((49 + -7i) + -1i * (-7 + i)) = 0
(49 + -7i + (-7 * -1i + i * -1i)) = 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}