# The Excel IMSECH Function

Related Functions:
IMSEC Function
IMCSCH Function
Hyperbolic Secant of a Complex Number

The hyperbolic secant of a complex number is defined as the inverse of the hyperbolic cosine.

I.e.

sech(z) = 1 / cosh(z)

## Function Description

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

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

The syntax of the function is:

IMSECH( inumber )

where the inumber argument is the complex number that you want to calculate the hyperbolic secant of.

### Complex Numbers in Excel

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

Column B of the following spreadsheet shows 4 different examples of the Imsech function. Each example uses a different method to supply the complex number to the function.

Formulas:
A B
1   =IMSECH( 0.5 )
2   =IMSECH( "3+0.5i" )
3 2-i =IMSECH( A3 )
4   =IMSECH( COMPLEX( 1, -1 ) )
Results:
A B
1   0.886818883970074
2   0.0873665779621302 - 0.0474925494901607i
3 2-i 0.151176298265577 + 0.226973675393722i
4   0.498337030555187 + 0.591083841721045i

Note that, in the above example spreadsheet:

• The real number 0.5, used in cell B1, is equal to the complex number 0.5+0i;
• The example in cell B4 uses the Excel Complex Function to create the complex number 1-i.

Further details and examples of the Excel Imsech function are provided on the Microsoft Office website

## Imsech Function Errors

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

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