# Calculation

## Using the application

### Doing a calculation

1. When you enter the Calculation application, the cursor is in the editing bar at the bottom of the screen. Enter your calculation in this edit bar.
2. Press the exe key. The calculation is performed.

When a calculation is performed, it is displayed at the bottom of the calculation history. In the history line corresponding to this calculation, you will see the calculation you typed in at the top left and the result at the bottom right. The exact result is displayed in black while the approximate numerical result is displayed in grey.

For more readability, the result of the calculations involving a decimal number is always given in decimal form: $0.1+0.3$ will give $0.4$ while $\frac{1}{10}+\frac{3}{10}$ will give $\frac{2}{5}$.

### Using the result of the immediately preceding calculation

You can use the exact result of the calculation you just performed in the expression of a new calculation. To do so, press ans. The expression ans is then displayed in the editing line and represents the result of the previous calculation. You can perform mathematical operations on this result.

### Using any result in the calculation history

To copy a previous result to the calculation editing bar, use the arrow keys to select the result you want to use (exact or approximate), then press ok. The result is then displayed in the editing bar at the bottom of the screen.

### Using the expression of a calculation already performed in the calculation history

You can copy the expression of a calculation that has already been performed to the calculation editing bar. To do so, select the expression of this calculation using the directional arrows. Then press ok, the expression of the calculation is then displayed in the edit bar at the bottom of the screen.

### Deleting a line in the history

To delete a line in the history, use the arrow keys to select an item from this line and press del.

To delete the entire history, select any item in the history using the arrow keys and use the clear function (shift then del).

## Performing calculations with complex numbers

### Choosing the complex format of the results

Your results can be displayed in rectangular or polar form (choose “real” to force the results to be real). Make this setting in the Settings application.

In rectangular form, the calculation of $\sqrt{-1}$ will give the result $i$. In polar form, the calculation of $\sqrt{-1}$ will give the result $e^{1.570796*i}$. In real form, the calculation of $\sqrt{-1}$ will give the result “unreal”.

In the polar form, the angle in the exponential is always given in radians, even if the calculator is set in degrees mode.

### Calculation of an expression with complex numbers

You can perform calculations with complex numbers as well as with real numbers. Your complex numbers can be typed in rectangular or polar form.

For example: if you type $i+e^{i*\frac{\pi}{2}}$, the result will be $2i$ if you are in rectangular mode and $2e^{i*\frac{\pi}{2}}$ if you are in polar mode.

### Absolute value, argument, real part, imaginary part, conjugate

You can calculate these values by using the shortcuts available in the Complex numbers section of the Toolbox menu to which you have access when you press the toolbox key.

You can also manually type the functions used to calculate these values. In the following list are the syntaxes of the corresponding functions :

• Absolute value : abs(z)
• Argument : arg(z)
• Real part : re(z)
• Imaginary part : im(z)
• Conjugate : conj(z)

## Performing calculations with matrices

### Typing a matrix using the keyboard

To type a matrix in the editing bar at the bottom of the screen, use the brackets [and ], accessible by pressing shift then exp or ln.

For example, type [[1,0][0,1]] to type the size 2 identity matrix :

$\left[\begin{array}{cc}1 & 0 \\\ 0 & 1 \end{array}\right]$

When you press ok, you can see your matrix displayed with the correct formatting in the calculation history.

It is useful to store matrices in variables. To do so, type your matrix then use the function sto → (by pressing shift then pow). Then type the name of the variable you want and press exe. For example, to store the size 2 identity matrix in variable M1, write [[1,0][0,1]] → M1 and press exe.

To make a capital letter press shift then alpha then press the key with the desired letter.

### Performing calculations

You can perform calculations between several matrices:

• Addition of two matrices: M1+M2
• Subtraction of two matrices: M1-M2
• Multiplication of two matrices (matrix product) : M1*M2
• Division of two matrices (inverse multiplication) : M1/M2 (corresponds to $M1*M2^{-1}$)

You can also perform calculations between a number and a matrix:

• Multiplication of a matrix by a scalar: 4*M1
• Power of a matrix: M1^5

### Inverse, determinant, transpose, trace, size

You can calculate these values by using the shortcuts available in the Matrix section of the Toolbox menu to which you have access when you press the toolbox key.

You can also manually type the functions used to calculate these values. In the following list are the syntaxes of the corresponding functions:

• Inverse : inverse(M)
• Determinant : det(M)
• Transpose : transpose(M)
• Trace : trace(M)
• Size : dim(M)