# Manual Reference Pages  - CATAN (3)

### NAME

catan, catanf, catanl - complex arc tangents

Synopsis
Description
Versions
Example
Colophon

### 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

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

#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); }