# The Excel IMCOT Function

Cotangent of a Complex Number

The cotangent of a complex number is defined as the inverse of the tangent.

I.e.

cot(z) = 1 / tan(z)

or

cot(z) = cos(z) / sin(z)
See Wikipedia for more information on complex numbers.

## Function Description

The Excel Imcot function returns the cotangent of a supplied complex number.

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

The syntax of the function is:

IMCOT( inumber )

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

## Imcot Function Examples

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

Formulas:
AB
1 =IMCOT( 0.5 )
2 =IMCOT( "3+0.5i" )
32-i=IMCOT( A3 )
4 =IMCOT( COMPLEX( 1, -1 ) )
Results:
AB
1 1.83048772171245
2 -0.479345578747373 - 2.01609252150623i
32-i-0.171383612909185 + 0.821329797493852i
4 0.217621561854403 + 0.868014142895925i

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 Imcot function are provided on the Microsoft Office website

## Imcot Function Errors

If you get an error from the Excel Imcot 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.