(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}