The Excel IMTAN Function

Tangent of a Complex Number

The tangent of a complex number is calculated by the following equation:

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

Function Description

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:

IMTAN( inumber )

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


Imtan Function Examples

In the spreadsheets below, the Excel Imtan function is used to calculate the tangent of 4 different complex numbers.

 Formulas:
 AB
1 =IMTAN( 0.5 )
2 =IMTAN( "3+0.5i" )
32-i=IMTAN( A3 )
4 =IMTAN( COMPLEX( 1, -1 ) )
 Results:
 AB
1 0.54630248984379
2 -0.111621050771583 + 0.469469993425885i
32-i-0.243458201185725 - 1.16673625724092i
4 0.271752585319512 - 1.08392332733869i

Note that, in the above example spreadsheet:


Further details and examples of the Excel Imtan function are provided on the Microsoft Office website


Imtan Function Errors

If you get an error from the Excel Imtan 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.