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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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