Complex Number Functions
========================

The `J' (`calc-conj') [`conj'] command computes the complex conjugate
of a number.  For complex number `a+bi', the complex conjugate is
`a-bi'.  If the argument is a real number, this command leaves it the
same.  If the argument is a vector or matrix, this command replaces
each element by its complex conjugate.

The `G' (`calc-argument') [`arg'] command computes the "argument" or
polar angle of a complex number.  For a number in polar notation, this
is simply the second component of the pair `(r;theta)'.  The result is
expressed according to the current angular mode and will be in the
range -180 degrees (exclusive) to +180 degrees (inclusive), or the
equivalent range in radians.

The `calc-imaginary' command multiplies the number on the top of the
stack by the imaginary number `i = (0,1)'.  This command is not
normally bound to a key in Calc, but it is available on the IMAG
button in Keypad Mode.

The `f r' (`calc-re') [`re'] command replaces a complex number by its
real part.  This command has no effect on real numbers.  (As an added
convenience, `re' applied to a modulo form extracts the value part.)

The `f i' (`calc-im') [`im'] command replaces a complex number by its
imaginary part; real numbers are converted to zero.  With a vector or
matrix argument, these functions operate element-wise.

The `v p' (`calc-pack') command can pack the top two numbers on the
the stack into a composite object such as a complex number.  With a
prefix argument of -1, it produces a rectangular complex number; with
an argument of -2, it produces a polar complex number.  (Also, *Note
Building Vectors::.)

The `v u' (`calc-unpack') command takes the complex number (or other
composite object) on the top of the stack and unpacks it into its
separate components.