> a:=(3+4*i)/(7-6*i);
                                      3 + 4 i
                                 a := -------
                                      7 - 6 i

> b:=simplify(a);
                                       3 + 4 i
                                b := - --------
                                       -7 + 6 i

> scalefrac(b,-1);
                                    3 + 4 i
                                    -------
                                    7 - 6 i

To see how the coordinates transform, you can use the plots:-conformal command:

a := 1:
cassinian := {NULL
              , x = a*2^(1/2)/2*((exp(2*u)+2*exp(u)*cos(v)+1)^(1/2) + exp(u)*cos(v)+1)^(1/2)
              , y = a*2^(1/2)/2*((exp(2*u)+2*exp(u)*cos(v)+1)^(1/2) - exp(u)*cos(v)-1)^(1/2)
             }:

# adjust the range to your liking...
plots:-conformal(subs(cassinian,u=Re(z),v=Im(z),x+I*y), z=map(`*`,0..1,5*(1+I)));

www.mathtable.com/gr/

www.mathtable.com/gr/

Glad to hear it works.

A pair of empty brackets ([]) appended to a list (or set) extracts the contents of the list (set).  See the 8th bullet in the help page for list.  For example

[a,b,c][];
                   a,b,c

You might, then, wonder why I bother to create a list if it is then immediately unpacked.  That is because one cannot do, for example, seq((a,b), i=1..3).  However, something I hadn't thought of is that we can use forward quotes to delay the evaluation and thus omit the brackets:

piecewise(seq('(x<=args[2*k+1],k)', k = 1..iquo(nargs,2)-1));

Glad to hear it works.

A pair of empty brackets ([]) appended to a list (or set) extracts the contents of the list (set).  See the 8th bullet in the help page for list.  For example

[a,b,c][];
                   a,b,c

You might, then, wonder why I bother to create a list if it is then immediately unpacked.  That is because one cannot do, for example, seq((a,b), i=1..3).  However, something I hadn't thought of is that we can use forward quotes to delay the evaluation and thus omit the brackets:

piecewise(seq('(x<=args[2*k+1],k)', k = 1..iquo(nargs,2)-1));

Most of my knowledge of Maple has been acquired by practice (i.e. using Maple, and trying stuff), reading the help pages, reading the programming manuals, inspecting existing code, and following this and other/previous Maple forums.

Most of my knowledge of Maple has been acquired by practice (i.e. using Maple, and trying stuff), reading the help pages, reading the programming manuals, inspecting existing code, and following this and other/previous Maple forums.

Examples of applying the common base types to arguments are give in the help page for evalapply. 

Examples of applying the common base types to arguments are give in the help page for evalapply. 

It's the "student mode" emulation 8-).

It's the "student mode" emulation 8-).

The empty function is an inert function whose name is `` and so appears as empty (invisible). For example,

``(a);
                     (a)

It can be used to group quantities that would otherwise be combined by Maple.  It's primary use is in ifactor, where it prevents the terms from being recombined:

ifactor(6);
                     (2)*(3)

The @ symbol is used for function composition (it is the closest non-letter ascii symbol corresponding to the usual mathematical symbol for function composition, the open centered circle).  Thus

(f@g)(x)
                    f(g(x))

Similary, (``@denom)(x) is equivalent to ``(denom(x)), which visually encloses the denominator of x in parentheses. Somewhat more elaborate is

makefrac := (``@numer)/(``@denom):

This works (as described herein) because with Maple one can apply an algebraic expression to arguments, the arguments are then passed to each of the algebraic terms.  For example (f/g)(x) evaluates to f(x)/g(x).  So makefrac(x) evaluates to ``(numer(x))/``(denom(x)) which then displays the numerator and denominator of x as a fraction, with no automatic recombination (numer and denom are designed to give the appropriate answer even if their arguments are not of type `*`).

The empty function is an inert function whose name is `` and so appears as empty (invisible). For example,

``(a);
                     (a)

It can be used to group quantities that would otherwise be combined by Maple.  It's primary use is in ifactor, where it prevents the terms from being recombined:

ifactor(6);
                     (2)*(3)

The @ symbol is used for function composition (it is the closest non-letter ascii symbol corresponding to the usual mathematical symbol for function composition, the open centered circle).  Thus

(f@g)(x)
                    f(g(x))

Similary, (``@denom)(x) is equivalent to ``(denom(x)), which visually encloses the denominator of x in parentheses. Somewhat more elaborate is

makefrac := (``@numer)/(``@denom):

This works (as described herein) because with Maple one can apply an algebraic expression to arguments, the arguments are then passed to each of the algebraic terms.  For example (f/g)(x) evaluates to f(x)/g(x).  So makefrac(x) evaluates to ``(numer(x))/``(denom(x)) which then displays the numerator and denominator of x as a fraction, with no automatic recombination (numer and denom are designed to give the appropriate answer even if their arguments are not of type `*`).

The problem I have with using CrossProduct is that it is restricted to 3D. Better to learn how to solve these with out that limitation.