| Types and the imaginary constant | |||||||||||||||||||||||||||||||
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| Manipulation | |||||||||||||||||||||||||||||||
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| Trigonometric functions | |||||||||||||||||||||||||||||||
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Defined in header <complex.h> | ||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (3) | (since C99) | |
Defined in header <tgmath.h> | ||
#define atan( z ) | (4) | (since C99) |
z with branch cuts outside the interval[−i,+i] along the imaginary axis.z has typelongdoublecomplex,catanl is called. ifz has typedoublecomplex,catan is called, ifz has typefloatcomplex,catanf is called. Ifz is real or integer, then the macro invokes the corresponding real function (atanf,atan,atanl). Ifz is imaginary, then the macro invokes the corresponding real version of the functionatanh, implementing the formulaatan(iy) = i atanh(y), and the return type of the macro is imaginary.Contents |
| z | - | complex argument |
If no errors occur, complex arc tangent ofz is returned, in the range of a strip unbounded along the imaginary axis and in the interval[−π/2; +π/2] along the real axis.
Errors and special cases are handled as if the operation is implemented by-I*catanh(I*z).
Inverse tangent (or arc tangent) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments(-∞i,-i) and(+i,+∞i) of the imaginary axis.
The mathematical definition of the principal value of inverse tangent isatan z = -| 1 |
| 2 |
#include <stdio.h>#include <float.h>#include <complex.h> int main(void){doublecomplex z= catan(2*I);printf("catan(+0+2i) = %f%+fi\n",creal(z),cimag(z)); doublecomplex z2= catan(-conj(2*I));// or CMPLX(-0.0, 2)printf("catan(-0+2i) (the other side of the cut) = %f%+fi\n",creal(z2),cimag(z2)); doublecomplex z3=2*catan(2*I*DBL_MAX);// or CMPLX(0, INFINITY)printf("2*catan(+0+i*Inf) = %f%+fi\n",creal(z3),cimag(z3));}
Output:
catan(+0+2i) = 1.570796+0.549306icatan(-0+2i) (the other side of the cut) = -1.570796+0.549306i2*catan(+0+i*Inf) = 3.141593+0.000000i
(C99)(C99)(C99) | computes the complex arc sine (function)[edit] |
(C99)(C99)(C99) | computes the complex arc cosine (function)[edit] |
(C99)(C99)(C99) | computes the complex tangent (function)[edit] |
(C99)(C99) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)[edit] |
C++ documentation foratan | |
