July 2, 2022

# How to use IMSECH Function in Excel

The IMSECH function returns the hyperbolic secant of a complex number in x+yi or x+yj text format. The hyperbolic secant of a complex number is defined as the inverse of the hyperbolic cosine i.e.

sech(z) = 1 / cosh(z)

Syntax:= IMSECH (inumber)

The IMSECH function syntax has the following arguments:

• Inumber: Required. A complex number for which you want the hyperbolic secant

Example: Let’s look at some Excel IMSECH function examples and explore how to use the IMSECH function as a worksheet function in Microsoft Excel: Syntax:  =IMSECH(A2)

Result: Based on the Excel spreadsheet above, the following IMSECH examples would return:

Syntax: =IMSECH(A3)
Result: -0.41314934426694+0.687527438655479i

Syntax: =IMSECH(A4)
Result: -0.00451692334111187+0.00204305005366211i

Syntax: =IMSECH(A5)
Result: 0.0897986028721219+0.137981006709971i

Syntax: =IMSECH(A6)
Result: -0.0362534969158689-0.00516434460775318i

Syntax: =IMSECH(A7)
Result: 2.35749526191317

Syntax: =IMSECH(A8)
Result: -0.000244349556680496-0.0000348311835455806i

Syntax: =IMSECH(A9)
Result: 0.0104002477656774+0.0351346130309063i

Syntax: =IMSECH(A10)
Result: 0.0000219408214556213-0.00495748625972705i

Syntax: =IMSECH(A11)
Result: 0.0113717647601419-0.00723019299882505i

Syntax: =IMSECH(A12)
Result: 0.0000370537940655624+0.0000828953005771029j

Syntax: =IMSECH(A13)
Result: 6.68625708732077E-11-1.94040887563525E-10i

Note:

• Complex Numbers in Excel are simply stored as text.
• 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.
• 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.
• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• If inumber is not recognized as a complex number, IMSECH returns the #NUM! error.
• If inumber is a logical value, IMSECH returns the #VALUE! error
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