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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'y'.

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

Simplifying
y = 1 + -1i2 + 2x + x2