complexExp function Null safety

Complex complexExp(
  1. Complex exponent
)

Calculate natural exponent for any number complex number: e^(x+(yi)). It's a generatlization of Euler’s formula: e^(iy) = cos(y) + i*sen(y).

  • exponent : a complex number

Examples

var c1 = Complex(real: 4.0, imaginary: 4.0);
print(complexExp(c1));

/* output:
Complex(real: -3.074932320639359, imaginary: 6.71884969742825)
*/

References

  1. "Understanding imaginary exponents". https://math.stackexchange.com/a/9777 . Retrieved 2021-05-10.
  2. "Exponential Form". https://tutorial.math.lamar.edu/Extras/ComplexPrimer/Forms.aspx . Retrieved 2021-05-10.
  3. "Euler's formula". https://en.wikipedia.org/wiki/Euler%27s_formula . Retrieved 2021-05-10.

Implementation

Complex complexExp(Complex exponent) {
  return Complex.ri(expFast(exponent.real) * math.cos(exponent.imaginary),
      expFast(exponent.real) * math.sin(exponent.imaginary));
}