# The Excel IMSEC Function

Secant of a Complex Number

The secant of a complex number is defined as the inverse of the cosine. I.e.

secant(z) = 1 / cosine(z)

## Function Description

The Excel Imsec function returns the secant of a supplied complex number.

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

The syntax of the function is:

IMSEC( inumber )

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

## Imsec Function Examples

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

Formulas:
AB
1 =IMSEC( 0.5 )
2 =IMSEC( "3+0.5i" )
32-i=IMSEC( A3 )
4 =IMSEC( COMPLEX( 1, -1 ) )
Results:
AB
1 1.13949392732455
2 -0.89191317974033 + 0.0587531781817398i
32-i-0.41314934426694 - 0.687527438655479i
4 0.498337030555187 - 0.591083841721045i

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 Imsec function are provided on the Microsoft Office website

## Imsec Function Errors

If you get an error from the Excel Imsec 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.