std.math.big.complex

Complex struct

Public Struct Complex Implements Equatable, Hashable, Printable, Numeric, Defaultable

Local i = Complex(0, 1)
Expect(i * i == Complex(-1, 0))
Expect(Complex(3, 4).Abs() == 5.0)
Expect(Complex(3, 4).Conjugate() == Complex(3, -4))
Expect(Complex(-4, 0).Sqrt() == Complex(0, 2))

std/math/big/complex.fb, line 44

• Public ReadOnly Field Real: Double field #

  Its real part.

• Public ReadOnly Field Imaginary: Double field #

  Its imaginary part.

• Public Static Method Zero(): Complex static method #

  The zero Complex, 0 + 0i, which adding leaves alone.

• Public Static Method One(): Complex static method #

  The Complex 1 + 0i, which multiplying leaves alone.

• Public Static Method DefaultValue(): Complex static method #

  The zero Complex, 0 + 0i.

• Public Static Method FromPolar(magnitude: Double, angle: Double): Complex static method #

  The number of the magnitude, at the angle in radians from the positive real axis, as cmath.rect gives it: an angle of 0 has a Real part of the magnitude, even an infinite one.

• Public Method ToString(): String method #

  "1+2i", "0-1.5i", or "-3+0i", the Imaginary part's sign always shown.

• Public Method Abs(): Double method #

  Its distance from 0.

• Public Method Arg(): Double method #

  Its angle from the positive real axis, from -pi to pi.

• Public Method Conjugate(): Complex method #

  The same number with its imaginary part negated.

• Public Method Exp(): Complex method #

  e to its power. A real number's is real, and one that a Double holds isn't infinite on the way, as e to past 709 would be.

• Public Method Log(): Complex method #

  Its natural logarithm: the log of its magnitude, and its Arg. Near a magnitude of 1, the log comes from log1p, which keeps the digits that log would lose; past a quarter of the largest Double, from half of it; and among the subnormals, from it scaled up by 2^53.

• Public Method Sqrt(): Complex method #

  Its square root with a Real part 0 or more, and the Imaginary part's sign, scaled as cmath scales it, so the largest and the subnormal numbers keep their digits.

• Public Method Pow(exponent: Complex): Complex method #

  It to the power: anything to 0 is 1, and 0 to a power with a Real part above 0 and no Imaginary part is 0, but to any other power has NaN parts.

• Operator ==(a: Complex, b: Complex): Bool operator #

  Whether a and b have equal real and imaginary parts.

• Operator ==(a: Complex, b: Double): Bool operator #

  Whether a and b are equal.

• Operator ==(a: Double, b: Complex): Bool operator #

  Whether a and b are equal.

• Public Method Hash(): UInt64 method #

  A hash of its two parts, which Complexes that are equal share.

• Operator +(a: Complex, b: Complex): Complex operator #

  a plus b.

• Operator +(a: Complex, b: Double): Complex operator #

  a plus b.

• Operator +(a: Double, b: Complex): Complex operator #

  a plus b.

• Operator -(a: Complex, b: Complex): Complex operator #

  a minus b.

• Operator -(a: Complex, b: Double): Complex operator #

  a minus b.

• Operator -(a: Double, b: Complex): Complex operator #

  a minus b.

• Operator *(a: Complex, b: Complex): Complex operator #

  a times b.

• Operator *(a: Complex, b: Double): Complex operator #

  a times b.

• Operator *(a: Double, b: Complex): Complex operator #

  a times b.

• Operator /(a: Complex, b: Complex): Complex operator #

  Smith's division, which scales by the larger part of b, so no product overflows on the way.

• Operator /(a: Complex, b: Double): Complex operator #

  a divided by b.

• Operator /(a: Double, b: Complex): Complex operator #

  a divided by b.

• Operator **(a: Complex, b: Int64): Complex operator #

  To a whole power, by squaring, which can be below 0.

• Operator -(a: Complex): Complex operator #

  a negated.