Java has no builtin support for complex numbers. To add or subtract two complex numbers you just add or subtract the corresponding real and imaginary parts.
// subtracting two complex numbers:
(a + ib)  (c + id) = (ab) + i(bd)
// multiplying two complex numbers:
(a + ib) * (c + id) = (ac  bd) + i(bc + ad)
// dividing two complex numbers:
(a + ib) / (c + id) = ((ac + bd) + i(bc  ad)) / (c² + d²)
// or in practice:
double bottom = 1.d / (c*c + d*d);
double real = (ac + bd) *
bottom;
double imaginary = (bc  ad)
* bottom;
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