C++ complex sin

The C++ complex ‘sin’ function compute the sine of the complex number.The declaration of the function is given below.

template<class T> complex<T> sin(const complex<T>& x);

Parameters:
x – A complex number whose sine is to be computed.

Return type
complex<T> -The complex sine of ‘x’.

Some points to note:

i) The sine is computed using the formula.

Code example

complex< double > c1(45.67 , 9.077);

cout<< sin( c1 ) ;

Output,

(4345.97,-510.399)

Explanation

The computation process of sin( c1 ) function is easy.Simply evaluate the equation,

sin( 45.67 )*cosh( 9.077 ) – icos( 45.67 )*sinh( 9.077 )

The complex number obtained is the sine complex of c1.The cos,sin , cosh and sinh functions are defined under the header <cmath> .

*Side Note

Some cases of sin function,

➥sin(conj(z) )=conj( sin(z) )

➥sin(±0 + i(±0)) , returns (±0 + i(±0)).

➥sin(±0 + iNaN) ,returns (±0 , iNaN).

➥sin(x + i∞ ) , returns (-∞ ,i(-∞) ),for some finite value ‘x’.

➥sin(-x – i∞ ) , returns (∞ , i∞ ) ,for some finite value ‘x’.

➥sin(±x + iNaN) ,returns NaN + iNaN , for some finite value ‘x’.

➥sin(±∞ + iy) ,returns NaN + iNaN ,for some finite value ‘y’.

➥sin(±∞ + i∞) ,returns (NaN , i(-∞)).

➥sin(±∞ + iNaN) ,returns NaN +iNaN

➥sin(NaN + iy) ,returns NaN +iNaN ,for some finite value ‘y’.

➥sin(NaN + i(±)∞) ,returns NaN + iNaN .

➥sin(NaN + iNaN) ,returns NaN+iNaN.