# The Excel IMCSC Function

Cosecant of a Complex Number

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

cosecant(z) = 1 / sine(z)

## Function Description

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

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

The syntax of the function is:

IMCSC( inumber )

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

## Imcsc Function Examples

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

Formulas:
AB
1 =IMCSC( 0.5 )
2 =IMCSC( "3+0.5i" )
32-i=IMCSC( A3 )
4 =IMCSC( COMPLEX( 1, -1 ) )
Results:
AB
1 2.08582964293349
2 0.545986482481967 + 1.77001641530855i
32-i0.6354937992539 - 0.221500930850509i
4 0.621518017170428 + 0.303931001628427i

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 Imcsc function are provided on the Microsoft Office website

## Imcsc Function Errors

If you get an error from the Excel Imcsc 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.