(-9+i)(-9-i)=0

Solution for (-9+i)(-9-i)=0 equation:

Simplifying
(-9 + i)(-9 + -1i) = 0

Multiply (-9 + i) * (-9 + -1i)
(-9(-9 + -1i) + i(-9 + -1i)) = 0
((-9 * -9 + -1i * -9) + i(-9 + -1i)) = 0
((81 + 9i) + i(-9 + -1i)) = 0
(81 + 9i + (-9 * i + -1i * i)) = 0
(81 + 9i + (-9i + -1i2)) = 0

Combine like terms: 9i + -9i = 0
(81 + 0 + -1i2) = 0
(81 + -1i2) = 0

Solving
81 + -1i2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-81' to each side of the equation.
81 + -81 + -1i2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -1i2 = 0 + -81
-1i2 = 0 + -81

Combine like terms: 0 + -81 = -81
-1i2 = -81

Divide each side by '-1'.
i2 = 81

Simplifying
i2 = 81

Take the square root of each side:
i = {-9, 9}