# Entering Complex Numbers

To add a complex number select the [b]Complex Number[/b] tool from the 2[sup]nd[/sup] button and click on the screen.[br][br]NB Complex Numbers will be added as z[sub]1[/sub], z[sub]2[/sub], ... a the variable z is reserved for 3D graphing.[br][br]You can also type [b]z_2=2+3i [/b]in the input bar and press enter to add the complex number $z_1=2+3i$ [br][b][br]p=z_1*z_2 [/b]will find the product.  [br][b]q=z_1/z_2 [/b]will find the quotient[br][br]The command [b]ComplexRoot[f][/b] will display the complex roots of a polynomial function.

# Entering Matrices

Type [b]M={{1,3},{2,4}} [/b]in the input bar and press enter to add the matrix $\left(\begin{matrix}1\\2\end{matrix}\begin{matrix}3\\4\end{matrix}\right)$.[br]Type [b]N={{0,-1},{1,0}} [/b]in the input bar and press enter to add the matrix $\left(\begin{matrix}0\\1\end{matrix}\begin{matrix}-1\\0\end{matrix}\right)$.[br][b][br]P=M*N[/b] will find the product MN.[br] [br][b]A’=M*A [/b]will find the image of a point [b]A[/b] under the transformation defined by matrix [b]M[/b].[br][br]The command [b]ApplyMatrix[M,poly1][/b] will find the image of the polygon [b]poly1[/b] under the transformation defined by matrix [b]M[/b].

# Entering Vectors

Vectors can be created using the [b]Vector[/b] or [b]Vector from Point[/b] tools in the third[br]menu.[br][br][b]Vector[/b] joins two points [b]A[/b] and [b]B[/b] with the vector AB.  [br][br][b]Vector from Point[/b] will translate an existing vector so that it starts from a point.[br][br]Alternatively enter a set of coordinates with a lower-case name will create the object as a position vector, e.g. [b]v=(2,3,-1)[br][br]Line[A,v] [/b]will create a a line through point [b]A[/b] in the direction [b]v[/b].[br][br]Planes can be entered directly in Cartesian form: e.g. [b]2x+3y-z=2[/b].
##### Notes about the 3D view
[b]View > 3D Graphics [/b]displays the 3D view.[br][br]The toolbar in 3D view allows 3D objects to be created.[br][br]Tomove a point click on it once for the x & y directions and twice for the z[br]direction.[br][br]Objectsfrom the 2D view will be displayed in the x-y plane of the 3D view.

# Entering polar coordinates and curves

Polar coordinates are entered using a semi-colon: e.g. [b](3;pi/3)[/b][br][br]Polar curves can be entered directly: e.g. [b]r=3+2cos(θ)[br][/b]NB GeoGebra will plot negative values of r.[br][br]You can also use the command [b]Curve[(r;[b]θ[/b]),[b]θ[/b],start value, end value][br][/b]e.g. [b]Curve[(2 + sin(θ/2); θ), θ, 0, 4pi][/b]

# Entering Maclaurin series

[list=1][br][*]Enter a function for f(x) such as [b]f(x)=sin(x)[/b].[br] [br][/*][*]Add a slider select the [i]Integer[/i] option. [/*] [*]In the input bar enter: [b]TaylorPolynomial[f, 0, n][/b].[br] [br] [/*][/list]