(x-i)(x+i)=0

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

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

Reorder the terms:
(-1i + x)(x + i) = 0

Reorder the terms:
(-1i + x)(i + x) = 0

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

Reorder the terms:
((-1ix + -1i2) + x(i + x)) = 0
((-1ix + -1i2) + x(i + x)) = 0
(-1ix + -1i2 + (i * x + x * x)) = 0
(-1ix + -1i2 + (ix + x2)) = 0

Reorder the terms:
(-1ix + ix + -1i2 + x2) = 0

Combine like terms: -1ix + ix = 0
(0 + -1i2 + x2) = 0
(-1i2 + x2) = 0

Solving
-1i2 + x2 = 0

Solving for variable 'i'.

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

Add '-1x2' to each side of the equation.
-1i2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
-1i2 + 0 = 0 + -1x2
-1i2 = 0 + -1x2
Remove the zero:
-1i2 = -1x2

Divide each side by '-1'.
i2 = x2

Simplifying
i2 = x2

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