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