Complex Reference
Complex number
What it is #
Position in the hierarchy #
| Inherits from | — |
| Does | — |
| Inherited by | ComplexStr |
Routines #
Signatures are reproduced from the documentation, including their declared return types. A routine listed here is part of the type's published interface; whether Raku++ implements it is a separate question, answered by the examples below.
postfix i #
Adding a trailing i to a number literal makes it a Complex, for example:
method new #
multi method new(Real $re, Real $im --> Complex:D)Returns Complex:D.
Creates a new Complex object from real and imaginary parts. When created without arguments, both parts are considered to be zero.
method re #
method re(Complex:D: --> Real:D)Returns Real:D.
Returns the real part of the complex number.
method im #
method im(Complex:D: --> Real:D)Returns Real:D.
Returns the imaginary part of the complex number.
method reals #
method reals(Complex:D: --> Positional:D)Returns Positional:D.
Returns a two-element list containing the real and imaginary parts for this value.
method isNaN #
method isNaN(Complex:D: --> Bool:D)Returns Bool:D.
Returns true if the real or imaginary part is NaN (not a number).
method polar #
method polar(Complex:D: --> Positional:D)Returns Positional:D.
Returns a two-element list of the polar coordinates for this value, i.e. magnitude and angle in radians.
method floor #
method floor(Complex:D: --> Complex:D)Returns Complex:D.
Returns self.re.floor + self.im.floor. That is, each of the real and imaginary parts is rounded to the highest integer not greater than the value of that part.
method ceiling #
method ceiling(Complex:D: --> Complex:D)Returns Complex:D.
Returns self.re.ceiling + self.im.ceiling. That is, each of the real and imaginary parts is rounded to the lowest integer not less than the value of that part.
routine sign #
method sign(Complex:D: --> Complex:D)
multi sign(Complex:D $z --> Complex:D)Returns Complex:D.
Returns 0i if the absolute value of the complex number is 0. Otherwise returns the complex number divided by its absolute value (the unit complex number in the same direction as $z). Available as of 6.e language version (early implementation exists in Rakudo compiler 2023.02+).
method round #
multi method round(Complex:D: --> Complex:D)
multi method round(Complex:D: Real() $scale --> Complex:D)Returns Complex:D.
With no arguments, rounds both the real and imaginary parts to the nearest integer and returns a new Complex number. If $scale is given, rounds both parts of the invocant to the nearest multiple of $scale. Uses the same algorithm as Real.round on each part of the number.
method truncate #
method truncate(Complex:D: --> Complex:D)Returns Complex:D.
Removes the fractional part of both the real and imaginary parts of the number, using Real.truncate, and returns the result as a new Complex.
routine abs #
method abs(Complex:D: --> Num:D)
multi abs(Complex:D $z --> Num:D)Returns Num:D.
Returns the absolute value of the invocant (or the argument in sub form). For a given complex number $z the absolute value |$z| is defined as sqrt($z.re * $z.re + $z.im * $z.im).
method conj #
method conj(Complex:D: --> Complex:D)Returns Complex:D.
Returns the complex conjugate of the invocant (that is, the number with the sign of the imaginary part negated).
method sqrt #
method sqrt(Complex:D: --> Complex:D)Returns Complex:D.
Returns the complex square root of the invocant, i.e. the root where the real part is ≥ 0 and the imaginary part has the same sign as the imaginary part of the invocant.
method gist #
method gist(Complex:D: --> Str:D)Returns Str:D.
Returns a string representation of the form "1+2i", without internal spaces. (Str coercion also returns this.)
method raku #
method raku(Complex:D: --> Str:D)Returns Str:D.
Returns an implementation-specific string that produces an equivalent object when given to EVAL.
method Real #
multi method Real(Complex:D: --> Num:D)
multi method Real(Complex:U: --> Num:D)Returns Num:D.
Coerces the invocant to Num. If the imaginary part isn't approximately zero, coercion fails with X::Numeric::Real. The :D variant returns the result of that coercion. The :U variant issues a warning about using an uninitialized value in numeric context and then returns value 0e0.
sub infix:<**> #
multi infix:<**>(Complex:D \a, Complex:D \b --> Complex:D)
multi infix:<**>(Num(Real) \a, Complex:D \b --> Complex:D)
multi infix:<**>(Complex:D \a, Num(Real) \b --> Complex:D)Returns Complex:D.
The exponentiation operator coerces the second argument to Complex and calculates the left-hand-side raised to the power of the right-hand side. Since 6.d, either argument can be equal to zero.
Examples, run three ways #
Every example below comes from the official documentation, together with the output that documentation asserts. Each was then executed by Rakudo and by Raku++ when this page was built. Where the three agree, one result is shown; where they do not, all three are — because which of them is wrong is exactly the information worth having.
2 all-differ · 2 no-output · 14 ok · 1 rakupp-differs
class Complex is Cool does Numeric {}Not executed: the documentation states no expected output for this example.
say 2i; # same as Complex.new(0, 2); say 1-2e3i; # same as Complex.new(1, -2e3);
Not executed: the documentation states no expected output for this example.
my $complex = Complex.new(1, 1); say $complex; # OUTPUT: «1+1i»
1+1i
Documentation, Rakudo and Raku++ all agree.
say Complex.new; # OUTPUT: «0+0i»
0+0i
Documentation, Rakudo and Raku++ all agree.
say (3+5i).re; # OUTPUT: «3»
3
Documentation, Rakudo and Raku++ all agree.
say (3+5i).im; # OUTPUT: «5»
5
Documentation, Rakudo and Raku++ all agree.
say (3+5i).reals; # OUTPUT: «(3 5)»
(3 5)
Documentation, Rakudo and Raku++ all agree.
say (NaN+5i).isNaN; # OUTPUT: «True» say (7+5i).isNaN; # OUTPUT: «False»
True
False
Documentation, Rakudo and Raku++ all agree.
say (10+7i).polar; # OUTPUT: «(12.2065556157337 0.610725964389209)»
(12.2065556157337 0.610725964389209)
(12.206555615733702 0.6107259643892086)
[12.206555615733702 0.6107259643892086]
All three differ. Needs a human.
Not yet examined. Which of these is correct has not been established — do not treat either engine as settled here.
say (1.2-3.8i).floor; # OUTPUT: «1-4i»
1-4i
Documentation, Rakudo and Raku++ all agree.
say (1.2-3.8i).ceiling; # OUTPUT: «2-3i»
2-3i
Documentation, Rakudo and Raku++ all agree.
say (1.2-3.8i).round; # OUTPUT: «1-4i» say (1.256-3.875i).round(0.1); # OUTPUT: «1.3-3.9i»
1-4i
1.3-3.9i
1-4i
1.3-3.9i
1-4i
1-4i
Raku++ disagrees with both the documentation and Rakudo — a defect.
say (1.2-3.8i).truncate; # OUTPUT: «1-3i»
1-3i
Documentation, Rakudo and Raku++ all agree.
say (3+4i).abs; # OUTPUT: «5»
# sqrt(3*3 + 4*4) == 55
Documentation, Rakudo and Raku++ all agree.
say (1-4i).conj; # OUTPUT: «1+4i»
1+4i
Documentation, Rakudo and Raku++ all agree.
say (3-4i).sqrt; # OUTPUT: «2-1i» say (-3+4i).sqrt; # OUTPUT: «1+2i»
2-1i
1+2i
Documentation, Rakudo and Raku++ all agree.
say (1-4i).gist; # OUTPUT: «1-4i»
1-4i
Documentation, Rakudo and Raku++ all agree.
say (1-3i).raku; # OUTPUT: «<1-3i>»
<1-3i>
Documentation, Rakudo and Raku++ all agree.
say i ** i; # OUTPUT: «0.20787957635076193+0i» say 2 ** i; # OUTPUT: «0.7692389013639721+0.6389612763136348i» say i ** 2; # OUTPUT: «-1+1.2246467991473532e-16i» say 0 ** i; # OUTPUT: «0+0i» say 0i ** 0i; # OUTPUT: «1+0i»
0.20787957635076193+0i
0.7692389013639721+0.6389612763136348i
-1+1.2246467991473532e-16i
0+0i
1+0i
0.20787957635076193+0i
0.7692389013639721+0.6389612763136348i
-1+0i
0+0i
1+0i
0.20787957635076193+0i
0.7692389013639721+0.6389612763136348i
-1+1.2246467991473532e-16i
NaN+NaNi
1+0i
All three differ. Needs a human.
Not yet examined. Which of these is correct has not been established — do not treat either engine as settled here.