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.