From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fcexp.html | 66 +++++++++++++++++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcexp.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcexp.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcexp.html b/devdocs/c/numeric%2Fcomplex%2Fcexp.html new file mode 100644 index 00000000..a8c4195b --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcexp.html @@ -0,0 +1,66 @@ +

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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