Methods by type

Complex methods

Full

Pull apart a complex number — real & imaginary parts, conjugate, magnitude.

A Complex (see Number forms) carries a real and an imaginary part, and offers the usual methods to inspect and transform it.

Parts, conjugate, magnitude #

.re and .im are the real and imaginary parts; .conj flips the sign of the imaginary part; .abs is the magnitude.

say (3 + 4i).re;
say (3 + 4i).im;
say (3 + 4i).conj;
say (3 + 4i).abs;

Output

(3 + 4i).abs is 5 — the hypotenuse of the 3–4 right triangle.

Polar form #

.polar returns the number as a (magnitude, angle) pair — the magnitude is .abs, and the angle is measured in radians from the positive real axis.

my ($mag, $ang) = (3 + 4i).polar;
say $mag;
say $ang.round(0.0001);

Output

5
0.9273

Arithmetic #

The usual operators work on Complex values directly, combining real and imaginary parts for you.

say (1 + 1i) * (1 + 1i);
say (2 + 3i) + (1 - 1i);

Output

0+2i
3+2i

(1 + 1i)² is 0 + 2i — the imaginary parts multiply to -1, cancelling the real part.

Notes #

.re/.im are the parts, .conj the conjugate, .abs the magnitude, and .polar the (magnitude, angle) form.
The imaginary unit is the i postfix: 2i is 0+2i — see Number forms.
sqrt extends to Complex, so (1 + 0i).sqrt is 1+0i; taking sqrt of a real negative ((-1).sqrt) gives NaN, so start from a Complex for an imaginary root.