The IMCOSH function in Excel is a useful tool for those working with complex numbers. It calculates the hyperbolic cosine of a given complex number, providing insights into various mathematical and scientific applications. This function is particularly advantageous for engineers, physicists, and mathematicians dealing with complex variable analysis and transformations.

Syntax

IMCOSH(inumber)

• inumber: The complex number for which the hyperbolic cosine will be calculated. This can be either a complex number represented as a text string (e.g., “3+4i”) or a reference to a cell containing that complex number.

Example #1

=IMCOSH("3+4i")

This function computes the hyperbolic cosine of the complex number 3 + 4i and would yield a result around -3.853 + 27.034i representing the hyperbolic cosine value for this input.

Example #2

=IMCOSH(A1)

Assuming cell A1 contains the complex number “2-2i”, this formula calculates the hyperbolic cosine of that complex number, resulting in approximately -0.643 + 1.468i.

Example #3

=IMCOSH(6)

In this case, the function evaluates the hyperbolic cosine of the real number 6 (considered as a complex number with an imaginary part of 0). The result would be about 201.715, demonstrating that IMCOSH can also work with real numbers effectively.

Error handling

• VALUE!: This error occurs when the input is not a valid complex number or if it is given in a format that Excel cannot recognize.
• NAME?: This happens when the function name is typed incorrectly, so ensure that “IMCOSH” is spelled properly.

Conclusion

In summary, the IMCOSH function is a powerful and efficient way to calculate the hyperbolic cosine of complex numbers in Excel. Its application serves various disciplines, enabling quick calculations that support enhanced understanding in mathematical and engineering contexts. By utilizing this function, users can simplify what would otherwise be complex calculations in their work.