[edit]Parameters

[edit]Return value

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

[edit]Error handling and special values

Errors are reported consistent withmath_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• cexp(conj(z))==conj(cexp(z))
• Ifz is±0+0i, the result is1+0i
• Ifz isx+∞i (for any finite x), the result isNaN+NaNi andFE_INVALID is raised.
• Ifz isx+NaNi (for any finite x), the result isNaN+NaNi andFE_INVALID may be raised.
• Ifz is+∞+0i, the result is+∞+0i
• Ifz is-∞+yi (for any finite y), the result is+0cis(y)
• Ifz is+∞+yi (for any finite nonzero y), the result is+∞cis(y)
• Ifz is-∞+∞i, the result is±0±0i (signs are unspecified)
• Ifz is+∞+∞i, the result is±∞+NaNi andFE_INVALID is raised (the sign of the real part is unspecified)
• Ifz is-∞+NaNi, the result is±0±0i (signs are unspecified)
• Ifz is+∞+NaNi, the result is±∞+NaNi (the sign of the real part is unspecified)
• Ifz isNaN+0i, the result isNaN+0i
• Ifz isNaN+yi (for any nonzero y), the result isNaN+NaNi andFE_INVALID may be raised
• Ifz isNaN+NaNi, the result isNaN+NaNi

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

[edit]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 anentire function in the complex plane and has no branch cuts.

[edit]Example

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

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

[edit]References

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