MathGraph32 allows to calculate and represent complexe numbers.

You can use usual transcendant function on complex numbers, create a point via it’s affix in a frame, mesure the complex affix of a point in a frame, create complexe functions of one, two or three complex variables, recurrent sequences kind of $u_{n+1} = f(u_n)$ and graph these sequences.

A complex calculus can use every calculus or measure (real or complex) defined before.

If you want to use in a real calculus the real part, imaginary part, argument or module of a complex number, you must first create a real calculus via menu items *calculus - New Real calculus - Real part of a complex* or *calculus - New Real calculus - Imaginary part of a complex* or *calculus - New Real calculus - Principal complex argument* or *calculus - New Real calculus - Complex modulus*.

Example : Vous wish to visualize the image of the circle center O and radius 1 through the complex transformation associated to function defined by *f*(*z*) = *z* + 1/*z*^n where *n* est an integer lying between 1 and 10.

Use menu item *File _ New Figure with - Frame with vectors* and choose an orthonormal frame and vectors named *u* and *v*.

Use icon to create the circle of center O and through point I(point I is the edge of vector *u*. It’s name is hidden).

Use menu item *Calculus - New variable* to create a variable named *n* with 1 as mini value, 10 as maxi value, 1 as step and 2 as current value. Set the **Associated dialog** checkbox selected.

Use menu item *Calculus - New complex calculus - Complex function* to create a complex function of one varible named *t* with formula *t*+1/*t*^n.

Use menu item *Macro - New macro - Variable increment*. Click on the top left corner of the figure.

A dialog box pops up. In the field **Title** enter *Increment n*. Variable *n* is already selected. Validate with **OK**.

In the same way, create a macro decrementing variable *n* under the former one with menu item *Macro - New macro - Variable decrement*.

Use icon to create a value display of variable *n* (vous pouvez utiliser le bouton **Liste des valeurs** pour sélectionner *n*). In the **Starting string** editor enter *n=*.

With icon create a linked point to the circle previously created and use l’icone to give name M to this point.

Use menu *Calculus - Measure - Point affix* or icon to measure affix of point M (just click on M). This measure is represented as Aff(M,O,I,J).

Via menu item *Calculus - New complex calculus >> Complex calculus*, create a calculus named *z* with formula *Aff(M,O,I,J)* (You can use button **Values** ).

In the same way create a complex calculus named *z’* with formula *f*(*z*).

Use icon to create point with affix *z’* and name this point M’.

Now we have to create the locus iof point M’ generated by the positions of point M on the circle.

In the color palette, activate the red color.

Now use icon . Click first on point M’ then on M. In the dialog box popping up, set the checkbox **Closed locus** selected et ask for 300 points. Validate.

The figure is now ready.

You can see this figure underneath, activated by MathGraph32 JavaScript library.