complex : Java Glossary

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complex
Complex numbers are pairs of floats or doubles with x being the real part and y being the imaginary part. The imaginary part is though of as being multiplied by the √-1 and added to the real part. They can be thought of geometrically as points on the x/y plane. Complex numbers can also be thought of as points defined by polar coordinates consisting of an angle θ anticlockwise from the x axis and a radius r.

Java has no built-in support for complex numbers. To add or subtract two complex numbers you just add or subtract the corresponding real and imaginary parts.

// adding two complex numbers:
(a + ib) + (c + id) = (a+b) + i(b+d)

// subtracting two complex numbers:
(a + ib) - (c + id) = (a-b) + i(b-d)

// 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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