Complex Computations, Add, Subtract, etc.

To add two complex numbers x = x.r + i * x.i and y = y.r + i * y.i,

x + y = (x.r + y.r) + i * (x.i + y.i) = {x.r + y.r, x.i + y.i}

where {x.r + y.r, x.i + y.i} is the 2-dimensional vector equivalent.

To subtract:

x − y = {x.r − y.r, x.i − y.i}

To multiply:

x*y = {x.r*y.r − x.i*y.i, x.r*y.i + x.i*y.r}

To divide:

x/y = {(x.r*y.r + x.i*y.i)/y2, (x.i*y.r − x.r*y.i)/y2}
where y2 = y.r^2 + y.i^2 and y != 0.

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