Related Functions:

The IMSECH function returns the hyperbolic secant of a complex number in x+yi or x+yj text format.

  • This function was introduced in Excel 2013 and so is not available in earlier versions.

Syntax

=IMSECH(inumber)

Arguments

Argument Description
inumber A complex number for which you want the hyperbolic secant

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.

Examples

  A B C D
1 Data Formula Result Notes
2 3+4i =IMSECH(A2) -0.065294027857947+0.0752249603027732i Returns the hyperbolic secant of a complex number, 3+4i
3   =IMSECH(“3+4i”) -0.065294027857947+0.0752249603027732i  
4   =IMSECH(“2-i”) 0.151176298265577+0.226973675393722i  
5   =IMSECH(COMPLEX(4,1)) 0.0198041304666168-0.0308224192896954i  

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if the supplied inumber argument is a logical value
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number

The hyperbolic secant of a complex number is defined as the inverse of the hyperbolic cosine and is calculated as:  

    \[   sech(z) = \frac 1{cosh(z)}   \]

See Wikipedia for more information on complex numbers.