The Excel IMSECH Function

Related Functions:

IMSEC Function
IMCSCH Function

Hyperbolic Secant of a Complex Number

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

I.e.

sech(z) = 1 / cosh(z)

See Wikipedia for more information on complex numbers.

Function Description

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

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

The syntax of the function is:

IMSECH( inumber )

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

Imsech Function Examples

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

Formulas:

	A	B
1		=IMSECH( 0.5 )
2		=IMSECH( "3+0.5i" )
3	2-i	=IMSECH( A3 )
4		=IMSECH( COMPLEX( 1, -1 ) )

Results:

	A	B
1		0.886818883970074
2		0.0873665779621302 - 0.0474925494901607i
3	2-i	0.151176298265577 + 0.226973675393722i
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 Imsech function are provided on the Microsoft Office website

Imsech Function Errors

If you get an error from the Excel Imsech 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.

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