(-10+i)(-10-i)=

Solution for (-10+i)(-10-i)= equation:

Simplifying
(-10 + i)(-10 + -1i) = 0

Multiply (-10 + i) * (-10 + -1i)
(-10(-10 + -1i) + i(-10 + -1i)) = 0
((-10 * -10 + -1i * -10) + i(-10 + -1i)) = 0
((100 + 10i) + i(-10 + -1i)) = 0
(100 + 10i + (-10 * i + -1i * i)) = 0
(100 + 10i + (-10i + -1i2)) = 0

Combine like terms: 10i + -10i = 0
(100 + 0 + -1i2) = 0
(100 + -1i2) = 0

Solving
100 + -1i2 = 0

Solving for variable 'i'.

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

Add '-100' to each side of the equation.
100 + -100 + -1i2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1i2 = 0 + -100
-1i2 = 0 + -100

Combine like terms: 0 + -100 = -100
-1i2 = -100

Divide each side by '-1'.
i2 = 100

Simplifying
i2 = 100

Take the square root of each side:
i = {-10, 10}