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)

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.