A class representing complex numbers. Note that this is a simplified representation of a complex number, which does not implement the full mathematical notion of a complex number.
Create a new complex number with the given real and imaginary parts.
| real |
the real part |
| imag |
the imaginary part |
a new instance of Complex.
a = Complex(2, 5);a.real;a.imag;The real part of the number.
The imaginary part of the number.
the complex conjugate.
xxxxxxxxxxComplex(2, 9).conjugateComplex addition.
xxxxxxxxxxComplex(2, 9) + Complex(-6, 2)Complex subtraction
xxxxxxxxxxComplex(2, 9) - Complex(-6, 2)Complex multiplication
xxxxxxxxxxComplex(2, 9) * Complex(-6, 2)Complex division.
xxxxxxxxxxComplex(2, 9) / Complex(-6, 2)Complex exponentiation with base e.
xxxxxxxxxxexp(Complex(2, 9))xxxxxxxxxxexp(Complex(0, pi)) == -1 // Euler's formula: trueComplex self multiplication.
xxxxxxxxxxsquared(Complex(2, 1))complex triple self multiplication.
xxxxxxxxxxcubed(Complex(2, 1))Complex square root
returns the principal root
Complex(4, 1.neg).sqrt// compare...Complex(4, 1.neg).pow(2.reciprocal)Complex exponentiation
not implemented for all combinations - some are mathematically ambiguous.
xxxxxxxxxxComplex(0, 2) ** 6xxxxxxxxxx2.3 ** Complex(0, 2)xxxxxxxxxxComplex(2, 9) ** 1.2 // not definedthe comparison of just the real parts.
xxxxxxxxxxComplex(2, 9) < Complex(5, 1);the comparison assuming that the reals (floats) are fully embedded in the complex numbers
xxxxxxxxxxComplex(1, 0) == 1;Complex(1, 5) == Complex(1, 5);negation of both parts
xxxxxxxxxxComplex(2, 9).negthe reciprocal of a complex number
xxxxxxxxxxComplex(3, 4).reciprocal1 / Complex(3, 4) // same, but less efficientthe absolute value of a complex number is its magnitude.
xxxxxxxxxxComplex(3, 4).absdistance to the origin.
the distance to the origin.
the angle in radians.
Convert to a Point.
Convert to a Polar
real part as Integer.
real part as Float.
returns this
a hash value
print this on given stream
Basic example:
xxxxxxxxxxa = Complex(0, 1);a * a; // returns Complex(-1, 0);Julia set approximation:
xxxxxxxxxxf = { |z| z * z + Complex(0.70176, 0.3842) };(var n = 80, xs = 400, ys = 400, dx = xs / n, dy = ys / n, zoom = 3, offset = -0.5;var field = { |x| { |y| Complex(x / n + offset * zoom, y / n + offset * zoom) } ! n } ! n;w = Window("Julia set", bounds:Rect(200, 200, xs, ys)).front;w.view.background_(Color.black);w.drawFunc = { n.do { |x| n.do { |y| var z = field[x][y]; z = f.(z); field[x][y] = z; Pen.color = Color.gray(z.rho.linlin(-100, 100, 1, 0)); Pen.addRect( Rect(x * dx, y * dy, dx, dy) ); Pen.fill } }};fork({ 6.do { w.refresh; 2.wait } }, AppClock))