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Excel IMSECH function

The IMSECH function returns the hyperbolic secant of a complex number in the form x + yi or x + yj.

Note: You can apply the COMPLEX function to convert real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Syntax

IMSECH(inumber)

Arguments

  • inumber (required): The complex number for which you want the hyperbolic secant.

Remarks

1. As the IMSECH function was first introduced in Excel 2013, it is only available in Excel 2013 and later versions.
2. The argument can be supplied as any of the following:
-- A real number whose imaginary part is 0, e.g., 1 is a complex number 1+ 0i; Or a purely imaginary number whose real part is 0, e.g., i is a complex number 0 + 1i;
-- A cell reference that refers to a complex number;
-- A complex number enclosed in double quotation marks.
3. The #VALUE! error occurs if any of the supplied arguments is a logical value.
4. The #NUM! error occurs if “inumber” cannot be recognized as a complex number.

Return value

It returns a complex number as text.

Example

To calculate the hyperbolic secant of the complex numbers in the following table, you can do as follows.

Select a cell (say D6), enter the formula below and press the Enter key to get the hyperbolic secant of the first complex number. Select this result cell and then drag its AutoFill Handle down to get the rest of the results.

=IMSECH(B6)

Notes:

1) The complex number can be directly entered into the formula and needs to be enclosed in double quotation marks. So, the formula in D7 can be changed to:

=IMSECH ("10+5j")

2) The IMSECH function accepts only lowercase “i” and “j”.

Related Functions

Excel COMPLEX function
The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Excel IMSEC function
The IMSEC function returns the secant of a complex number in the form x + yi or x + yj.

Excel IMSIN function
The IMSIN function returns the sine of a complex number in the form x + yi or x + yj.

Excel IMSINH function
The IMSINH function returns the hyperbolic sine of a complex number in the form x + yi or x + yj.

Excel IMSQRT Function
The IMSQRT function returns the square root of a complex number in the form x + yi or x + yj.

Excel IMTAN function
The IMTAN function returns the tangent of a given complex number in the form x + yi or x + yj.

Excel IMSUB function
The IMSUB function returns the difference of two complex numbers in x + yi or x + yj text format.


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