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cexpf, cexp, cexpl

Defined in header <complex.h> 
float complex       cexpf( float complex z );
-		 (1) (since C99) 
double complex      cexp( double complex z );
-		 (2) (since C99) 
long double complex cexpl( long double complex z );
-		 (3) (since C99)
Defined in header <tgmath.h> 
#define exp( z )
-		 (4) (since C99)
-1-3) Computes the complex base-e exponential of z.
-4) Type-generic macro: If z has type long double complex, cexpl is called. if z has type double complex, cexp is called, if z has type float complex, cexpf is called. If z is real or integer, then the macro invokes the corresponding real function (expf, exp, expl). If z is imaginary, the corresponding complex argument version is called.

Parameters

- -
z - complex argument

Return value

If no errors occur, e raised to the power of z, \(\small e^z\)ez is returned.

-

Error handling and special values

Errors are reported consistent with math_errhandling.

-

If the implementation supports IEEE floating-point arithmetic,

-

where \(\small{\rm cis}(y)\)cis(y) is \(\small \cos(y)+{\rm i}\sin(y)\)cos(y) + i sin(y)

-

Notes

The complex exponential function \(\small e^z\)ez for \(\small z = x + {\rm i}y\)z = x+iy equals \(\small e^x {\rm cis}(y)\)ex cis(y), or, \(\small e^x (\cos(y)+{\rm i}\sin(y))\)ex (cos(y) + i sin(y))

-

The exponential function is an entire function in the complex plane and has no branch cuts.

-

Example

#include <stdio.h>
-#include <math.h>
-#include <complex.h>
- 
-int main(void)
-{
-    double PI = acos(-1);
-    double complex z = cexp(I * PI); // Euler's formula
-    printf("exp(i*pi) = %.1f%+.1fi\n", creal(z), cimag(z));
- 
-}

Output:

-
exp(i*pi) = -1.0+0.0i

References

See also

- - -
-
(C99)(C99)(C99)
 computes the complex natural logarithm
(function)
-
(C99)(C99)
 computes e raised to the given power (\({\small e^x}\)ex)
(function)
C++ documentation for exp
-

- © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
- https://en.cppreference.com/w/c/numeric/complex/cexp -

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