The J (
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 (
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
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.
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 (
re] command replaces a complex number
by its real part. This command has no effect on real numbers. (As an
re applied to a modulo form extracts
the value part.)
The f i (
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 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, see 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.