4.4.4.1 ComplexNumber Objects

class ComplexNumber
A complex number.
ComplexNumber( real, [imag=0], [prec=None])

Instances of class ComplexNumber have the following methods (in addition to inherited methods and special methods):

arg,$  $ argument,$  $ exp,$  $ log

These methods are defined as follows:

arg( )

Same as argument.

argument( )

The argument (angle) of the complex number, normalized so that -pi < arg <= pi.

WARNING: We use the floating point atan function, so there is precision loss.

exp( [prec=None])

Compute exp(z) using Fourier series.

If prec is given, compute until the nth summand is less than $ 10^{-prec}$ .

log( )

Complex logarithm of z with branch chosen as follows: Write z = rho*exp(i*theta) with -pi <= theta < pi. Then log(z) = log(rho) + i*theta.

WARNING: Currently the real log is computed using floats, so there is potential precision loss.

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