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
