y=(x+1+2i)(x+1-2i)

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Solution for y=(x+1+2i)(x+1-2i) equation:


Simplifying
y = (x + 1 + 2i)(x + 1 + -2i)

Reorder the terms:
y = (1 + 2i + x)(x + 1 + -2i)

Reorder the terms:
y = (1 + 2i + x)(1 + -2i + x)

Multiply (1 + 2i + x) * (1 + -2i + x)
y = (1(1 + -2i + x) + 2i * (1 + -2i + x) + x(1 + -2i + x))
y = ((1 * 1 + -2i * 1 + x * 1) + 2i * (1 + -2i + x) + x(1 + -2i + x))
y = ((1 + -2i + 1x) + 2i * (1 + -2i + x) + x(1 + -2i + x))
y = (1 + -2i + 1x + (1 * 2i + -2i * 2i + x * 2i) + x(1 + -2i + x))

Reorder the terms:
y = (1 + -2i + 1x + (2i + 2ix + -4i2) + x(1 + -2i + x))
y = (1 + -2i + 1x + (2i + 2ix + -4i2) + x(1 + -2i + x))
y = (1 + -2i + 1x + 2i + 2ix + -4i2 + (1 * x + -2i * x + x * x))

Reorder the terms:
y = (1 + -2i + 1x + 2i + 2ix + -4i2 + (-2ix + 1x + x2))
y = (1 + -2i + 1x + 2i + 2ix + -4i2 + (-2ix + 1x + x2))

Reorder the terms:
y = (1 + -2i + 2i + 2ix + -2ix + -4i2 + 1x + 1x + x2)

Combine like terms: -2i + 2i = 0
y = (1 + 0 + 2ix + -2ix + -4i2 + 1x + 1x + x2)
y = (1 + 2ix + -2ix + -4i2 + 1x + 1x + x2)

Combine like terms: 2ix + -2ix = 0
y = (1 + 0 + -4i2 + 1x + 1x + x2)
y = (1 + -4i2 + 1x + 1x + x2)

Combine like terms: 1x + 1x = 2x
y = (1 + -4i2 + 2x + x2)

Solving
y = 1 + -4i2 + 2x + x2

Solving for variable 'y'.

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

Simplifying
y = 1 + -4i2 + 2x + x2

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