Complex Numbers
===============

There are two supported formats for complex numbers: rectangular and
polar.  The default format is rectangular, displayed in the form
`(REAL,IMAG)' where REAL is the real part and IMAG is the imaginary
part, each of which may be any real number.  Rectangular complex
numbers can also be displayed in `A+Bi' notation; *Note Complex
Formats::.

Polar complex numbers are displayed in the form `(R;THETA)'
where R is the nonnegative magnitude and THETA is the argument
or phase angle.  The range of THETA depends on the current angular
mode (See Angular Modes); it is generally between -180 and
+180 degrees or the equivalent range in radians.

Complex numbers are entered in stages using incomplete objects.
See Incomplete Objects.

Operations on rectangular complex numbers yield rectangular complex
results, and similarly for polar complex numbers.  Where the two types
are mixed, or where new complex numbers arise (as for the square root
of a negative real), the current "Polar Mode" is used to determine the
type.  See Polar Mode.

A complex result in which the imaginary part is zero (or the phase
angle is 0 or 180 degrees or `pi' radians) is automatically converted
to a real number.