## Name

catan, catanf, catanl — complex arc tangents

## Synopsis

```#include <complex.h>
```
 ```double complex catan(``` double complex z`)`;

 ```float complex catanf(``` float complex z`)`;

 ```long double complex catanl(``` long double complex z`)`;

Note Link with `−lm`.

## DESCRIPTION

The `catan`() function calculates the complex arc tangent of `z`. If y = catan(z), then z = ctan(y). The real part of y is chosen in the interval [−pi/2,pi/2].

One has:

```    catan(z) = (clog(1 + i * z) − clog(1 − i * z)) / (2 * i)
```

## VERSIONS

These functions first appeared in glibc in version 2.1.

C99.

## EXAMPLE

```/* Link with "−lm" */

#include <complex.h>
#include <stdlib.h>
#include <unistd.h>
#include <stdio.h>

int
main(int argc, char *argv[])
{
double complex z, c, f;
double complex i = I;

if (argc != 3) {
fprintf(stderr, "Usage: %s <real> <imag>\n", argv[0]);
exit(EXIT_FAILURE);
}

z = atof(argv[1]) + atof(argv[2]) * I;

c = catan(z);
printf("catan() = %6.3f %6.3f*i\n", creal(c), cimag(c));

f = (clog(1 + i * z) − clog(1 − i * z)) / (2 * i);
printf("formula = %6.3f %6.3f*i\n", creal(f2), cimag(f2));

exit(EXIT_SUCCESS);
}
```

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