(10+5i)(10-5i)=

Solution for (10+5i)(10-5i)= equation:

Simplifying
(10 + 5i)(10 + -5i) = 0

Multiply (10 + 5i) * (10 + -5i)
(10(10 + -5i) + 5i * (10 + -5i)) = 0
((10 * 10 + -5i * 10) + 5i * (10 + -5i)) = 0
((100 + -50i) + 5i * (10 + -5i)) = 0
(100 + -50i + (10 * 5i + -5i * 5i)) = 0
(100 + -50i + (50i + -25i2)) = 0

Combine like terms: -50i + 50i = 0
(100 + 0 + -25i2) = 0
(100 + -25i2) = 0

Solving
100 + -25i2 = 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 + -25i2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -25i2 = 0 + -100
-25i2 = 0 + -100

Combine like terms: 0 + -100 = -100
-25i2 = -100

Divide each side by '-25'.
i2 = 4

Simplifying
i2 = 4

Take the square root of each side:
i = {-2, 2}