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Function std.complex.pow

Calculates xn. The branch cut is on the negative axis.

Complex!T pow(T, Int) (
  Complex!T x,
  const Int n
) pure nothrow @nogc @safe
if (isIntegral!Int);

Complex!T pow(T) (
  Complex!T x,
  const T n
) pure nothrow @nogc @trusted;

Complex!T pow(T) (
  Complex!T x,
  Complex!T y
) pure nothrow @nogc @trusted;

Complex!T pow(T) (
  const T x,
  Complex!T n
) pure nothrow @nogc @trusted;

Parameters

NameDescription
x base
n exponent

Returns

x raised to the power of n

Example

import std.math.operations : isClose;

auto a = complex(1.0, 2.0);
writeln(pow(a, 2)); // a * a
writeln(pow(a, 3)); // a * a * a
writeln(pow(a, -2)); // 1.0 / (a * a)
assert(isClose(pow(a, -3), 1.0 / (a * a * a)));

auto b = complex(2.0);
assert(ceqrel(pow(b, 3), exp(3 * log(b))) >= double.mant_dig - 1);

Example

import std.math.operations : isClose;
writeln(pow(complex(0.0), 2.0)); // complex(0.0)
writeln(pow(complex(5.0), 2.0)); // complex(25.0)

auto a = pow(complex(-1.0, 0.0), 0.5);
assert(isClose(a, complex(0.0, +1.0), 0.0, 1e-16));

auto b = pow(complex(-1.0, -0.0), 0.5);
assert(isClose(b, complex(0.0, -1.0), 0.0, 1e-16));

Example

import std.math.operations : isClose;
import std.math.exponential : exp;
import std.math.constants : PI;
auto a = complex(0.0);
auto b = complex(2.0);
writeln(pow(a, b)); // complex(0.0)

auto c = complex(0.0L, 1.0L);
assert(isClose(pow(c, c), exp((-PI) / 2)));

Example

import std.math.operations : isClose;
writeln(pow(2.0, complex(0.0))); // complex(1.0)
writeln(pow(2.0, complex(5.0))); // complex(32.0)

auto a = pow(-2.0, complex(-1.0));
assert(isClose(a, complex(-0.5), 0.0, 1e-16));

auto b = pow(-0.5, complex(-1.0));
assert(isClose(b, complex(-2.0), 0.0, 1e-15));

Authors

Lars Tandle Kyllingstad, Don Clugston

License

Boost License 1.0