The cotangent of a complex number is defined as the inverse of the tangent.
I.e.
or
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:
where the inumber argument is the complex number that you want to calculate the cotangent of.
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 builtin 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.
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:

Results:

Note that, in the above example spreadsheet:
Further details and examples of the Excel Imcot function are provided on the Microsoft Office website
If you get an error from the Excel Imcot Function, this is likely to be one of the following:
#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. 