IMSECH Function

Basic Description

The Excel Imsech function returns the hyperbolic secant of a supplied complex number.

Note: the Imsech function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.

Syntax: IMSECH( inumber )

where the inumber argument is a complex number.

Note that complex numbers are simply stored as text in Excel. When a text string in the format “a+bi” or “a+bj” is supplied to one of Excel’s built-in complex number functions, this is interpreted as a complex number. Also the complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.


Imsech Function Examples

The spreadsheet below shows 4 different examples of the Imsech function. Each example uses a different method to supply the complex number to the function.

1 =IMSECH( 0.5 )
2 =IMSECH( “3+0.5i” )
3 2 – i =IMSECH( A3 )
4 =IMSECH( COMPLEX( 1, -1 ) )
1 0.886818883970074
2 0.0873665779621302 – 0.0474925494901607i
3 2 – i 0.151176298265577 + 0.226973675393722i
4 0.498337030555187 + 0.591083841721045i

Note that, in cell B1 of the above spreadsheet, the supplied inumber argument is the real number 0.5, which is equal to the complex number 0.5+0i.


Imsech Function Errors

If you get an error from the Excel Imsech Function, this is likely to be one of the following:

#VALUE! Occurs if the supplied inumber argument is a logical value.
#NUM! Occurs if the supplied inumber argument is not recognised as a complex number.

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