The tangent of a complex number is calculated by the following equation:
The Excel Imtan function returns the tangent of a supplied complex number.
Note: the Imtan 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 tangent 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.
In the spreadsheets below, the Excel Imtan function is used to calculate the tangent of 4 different complex numbers.
Formulas:

Results:

Note that, in the above example spreadsheet:
Further details and examples of the Excel Imtan function are provided on the Microsoft Office website
If you get an error from the Excel Imtan 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. 