f(x)=(x-1+i)(x-1-i)

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Solution for f(x)=(x-1+i)(x-1-i) equation: 


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

Multiply f * x
fx = (x + -1 + i)(x + -1 + -1i)

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

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

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

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

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

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

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

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

Combine like terms: -1x + -1x = -2x
fx = (1 + -1i2 + -2x + x2)

Solving
fx = 1 + -1i2 + -2x + x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = x-1 + -1i2x-1 + -2 + x

Simplifying
f = x-1 + -1i2x-1 + -2 + x

Reorder the terms:
f = -2 + -1i2x-1 + x-1 + x

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