(-5+i)(-5-i)=

Solution for (-5+i)(-5-i)= equation:

Simplifying
(-5 + i)(-5 + -1i) = 0

Multiply (-5 + i) * (-5 + -1i)
(-5(-5 + -1i) + i(-5 + -1i)) = 0
((-5 * -5 + -1i * -5) + i(-5 + -1i)) = 0
((25 + 5i) + i(-5 + -1i)) = 0
(25 + 5i + (-5 * i + -1i * i)) = 0
(25 + 5i + (-5i + -1i2)) = 0

Combine like terms: 5i + -5i = 0
(25 + 0 + -1i2) = 0
(25 + -1i2) = 0

Solving
25 + -1i2 = 0

Solving for variable 'i'.

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

Add '-25' to each side of the equation.
25 + -25 + -1i2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1i2 = 0 + -25
-1i2 = 0 + -25

Combine like terms: 0 + -25 = -25
-1i2 = -25

Divide each side by '-1'.
i2 = 25

Simplifying
i2 = 25

Take the square root of each side:
i = {-5, 5}