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

Solution for (1-i)(1+i)=0 equation:

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

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

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

Solving
1 + -1i2 = 0

Solving for variable 'i'.

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

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

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

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

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

Simplifying
i2 = 1

Take the square root of each side:
i = {-1, 1}