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 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.