Calculabo

An elegant yet powerful calculator app.

# Complex numbers

Calculabo has full support for complex numbers. All built-in functions, operators and storage objects that work with real numbers, are also compatible with complex numbers.

## Imaginary unit

By default, the imaginary unit is available under variable $i$, which is defined as $+√−1$. You can continue working with complex numbers even if you assign a different value to $i$.

## Cartesian and polar coordinates

You can extract the cartesian coordinates of any complex number using the built-in functions $Re$ (or $real$) for the real component and $Im$ (or $imag$) for the imaginary component. For polar coordinates, you use $abs$ for the absolute value and $arg$ (or $angle$) for the argument.

### Example

$x≔3+√−16$
$3+4i$
$[Re(x),Im(x);abs(x),arg(x)]$
$[3,4;5,0.927295218001612]$

These functions also accept matrices: in this case, all elements are transformed individually.

### Example

$arg([−1,0,1;−i,0,i])$
$[3.14159265358979,¿,0;−1.5707963267949,¿,1.5707963267949]$

Note that the argument of zero is indeterminate ($¿$).

## Sign

The sign of a complex number is defined as the number divided by its absolute value, or $0$ if the number is zero. Use the function $sgn$ (or $sign$) to get it.

### Example

$sgn(3+4i)$
$0.6+0.8i$

Like the functions above, matrices are transformed element-wise. Calculabo has no matrix sign function!