Excel IMCOSH Function
The IMCOSH function returns the hyperbolic cosine value of a given complex number in x + yi or x + yj text format.
Note: The IMCOSH function was introduced in Excel 2013. So, it is not available in earlier versions of Excel.
Syntax
=IMCOSH(inumber)
Arguments
- inumber (required): A complex number for which to calculate the hyperbolic cosine value.
Return Value
The IMCOSH function returns a complex number as text.
Function Notes
- inumber 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.
- inumber can be returned by the COMPLEX function which converts real and imaginary coefficients into a complex number.
- IMCOSH will return the #NUM! error if inumber is not recognized as a complex number that has lowercase i or j (iota).
- IMCOSH will return the #VALUE! error if inumber is a logical value.
- The hyperbolic cosine of a complex number is:
cosh(x + yi) = cos(y)cosh(x) + sin(y)sinh(x)i
OR
cosh(x + yj) = cos(y)cosh(x) + sin(y)sinh(x)j
Example
To calculate the hyperbolic cosine of the complex numbers listed in the below table, please copy or enter the formula below in the top cell, press Enter to get the result, and then drag the fill handle (at the lower right corner of the result cell) down to apply the formula to below cells.
=IMCOSH(B3)
Also, you can type the actual complex number in the formula as shown below. Make sure the complex number is enclosed with double quotes:
=IMCOSH("3+4i")
Related functions
The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.
The IMCOS function returns the cosine value of a given complex number in x + yi or x + yj text format.
The IMCOT function returns the cotangent value of a given complex number in x + yi or x + yj text format.
The IMCSC function returns the cosecant value of a given complex number in x + yi or x + yj text format.
The IMCSCH function returns the hyperbolic cosecant value of a given complex number in x + yi or x + yj text format.
The IMSEC function returns the secant value of a given complex number in x + yi or x + yj text format.
The IMSECH function returns the hyperbolic secant value of a given complex number in x + yi or x + yj text format.
The IMSIN function returns the sine value of a given complex number in x + yi or x + yj text format.
The IMSINH function returns the hyperbolic sine value of a given complex number in x + yi or x + yj text format.
The IMTAN function returns the tangent value of a given complex number in x + yi or x + yj text format.
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