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# The Complex class.

Class `Complex` is implemented in a way similar to that described by Stroustrup. In keeping with libg++ conventions, the class is named `Complex`, not `complex`. Complex arithmetic and relational operators are provided (`+, -, *, /, +=, -=, *=, /=, ==, !=`). Attempted division by (0, 0) triggers an exception.

Complex numbers may be constructed and used in the following ways:

`Complex x;`
  Declares an uninitialized Complex.
`Complex x = 2; Complex y(2.0);`
  Set x and y to the Complex value (2.0, 0.0);
`Complex x(2, 3);`
  Sets x to the Complex value (2, 3);
`Complex u(x); Complex v = x;`
  Set u and v to the same value as x.
`double real(Complex& x);`
  returns the real part of x.
`double imag(Complex& x);`
  returns the imaginary part of x.
`double abs(Complex& x);`
  returns the magnitude of x.
`double norm(Complex& x);`
  returns the square of the magnitude of x.
`double arg(Complex& x);`
  returns the argument (amplitude) of x.
`Complex polar(double r, double t = 0.0);`
  returns a Complex with abs of r and arg of t.
`Complex conj(Complex& x);`
  returns the complex conjugate of x.
`Complex cos(Complex& x);`
  returns the complex cosine of x.
`Complex sin(Complex& x);`
  returns the complex sine of x.
`Complex cosh(Complex& x);`
  returns the complex hyperbolic cosine of x.
`Complex sinh(Complex& x);`
  returns the complex hyperbolic sine of x.
`Complex exp(Complex& x);`
  returns the exponential of x.
`Complex log(Complex& x);`
  returns the natural log of x.
`Complex pow(Complex& x, long p);`
  returns x raised to the p power.
`Complex pow(Complex& x, Complex& p);`
  returns x raised to the p power.
`Complex sqrt(Complex& x);`
  returns the square root of x.
`ostream << x;`
  prints x in the form (re, im).
`istream >> x;`
  reads x in the form (re, im), or just (re) or re in which case the imaginary part is set to zero.

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