The C++ complex ‘asinh’ function compute the arc hyperbolic sine of the complex number.The declaration of the function is given below.
|template<class T> complex<T> asinh(const complex<T>& x);|
x – A complex number whose arc hyperbolic sine is to be computed.
complex<T> -The complex arc hyperbolic sine of ‘x’.
Some points to note:
i)The arc hyperbolic sine is computed using the formula.
ii)The asinh functions compute the complex arc hyperbolic sine of x,with branch cuts outside the interval [−i , +i] along the imaginary axis.
iii)The ‘asinh’ returns a complex whose value is in the range of a half-strip of non-negative values along the real axis and in the interval [−iπ , +iπ] along the imaginary axis.
cout<< asinh( c1 +c2 ) ;
The c1+c2 is (923.5,8.023),to find the asinh(923.5,8.023 ) we use the equation given below,
ln[ (923.5+i8.023) ± √((2.34 + i6.78)2 + 1) ]
The ‘ln’ is the natural logarithm which is also written as ‘loge‘.Reducing the equation to the complex number form we get “7.52136 + i0.00868738” as the resultant complex value.
Link :C++ cmath log function
Some cases of asinh function,
➥asinh( conj(z) )=conj( asinh(z) ).
➥asinh(+0 + i0) returns 0+i0.
➥asinh(±0 + iNaN) ,returns (±NaN , iNaN).
➥asinh(x + i∞) returns +∞ + iπ/2 for positive-signed finite ‘x’.
➥asinh(x + iNaN) returns NaN+iNaN and optionally raises the invalid floating-point exception, for finite ‘x’.
➥asinh(+∞ + iy) returns +∞ +i0 for positive-signed finite ‘y’.
➥asinh(+∞ + i∞ ) returns +∞ + iπ/4
➥asinh(+∞ +iNaN) returns +∞ +iNaN.
➥asinh(NaN + i0) returns NaN+i0.
➥asinh(NaN + iy) returns NaN+iNaN and optionally raises the “invalid” floating-point exception, for finite nonzero ‘y’.
➥asinh(NaN + i∞) returns ±∞ +iNaN (where the sign of the real part of the resultis unspecified)
➥asinh(NaN + iNaN) returns NaN+iNaN.
Link :C++ complex conj