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# catan - Man Page

complex arc tangents

## Library

Math library (libm, -lm)

## Synopsis

```#include <complex.h>

double complex catan(double complex z);
float complex catanf(float complex z);
long double complex catanl(long double complex z);```

## Description

These functions calculate 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)`

## Attributes

For an explanation of the terms used in this section, see attributes(7).

InterfaceAttributeValue

## Standards

C11, POSIX.1-2008.

## History

glibc 2.1. C99, POSIX.1-2001.

## Examples

```/* Link with "-lm" */

#include <complex.h>
#include <stdio.h>
#include <stdlib.h>
#include <unistd.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(f), cimag(f));

exit(EXIT_SUCCESS);
}```