# The Excel IMTAN Function

Related Functions:
IMCOS Function
IMSIN Function
Tangent of a Complex Number

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

tan(z) = sin(z) / cos(z)

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

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 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.