# The Excel IMCSCH Function

Hyperbolic Cosecant of a Complex Number

The hyperbolic cosecant of a complex number is defined as the inverse of the hyperbolic sine.

I.e.

csch(z) = 1 / sinh(z)
See Wikipedia for more information on complex numbers.

## Function Description

The Excel Imcsch function returns the hyperbolic cosecant of a supplied complex number.

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

The syntax of the function is:

IMCSCH( inumber )

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

## Imcsch Function Examples

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

Formulas:
AB
1 =IMCSCH( 0.5 )
2 =IMCSCH( "3+0.5i" )
32-i=IMCSCH( A3 )
4 =IMCSCH( COMPLEX( 1, -1 ) )
Results:
AB
1 1.91903475133494
2 0.0874014937786455 - 0.0479849510697105i
32-i0.141363021612408 + 0.228375065599687i
4 0.303931001628426 + 0.621518017170429i

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 Imcsch function are provided on the Microsoft Office website

## Imcsch Function Errors

If you get an error from the Excel Imcsch 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.