The IMSECH function in Google Sheets is a powerful tool for performing hyperbolic calculations involving complex numbers. It enables users to easily obtain the hyperbolic secant of input values formatted as complex numbers, which can be particularly useful in fields such as engineering and physics, where complex analysis is often applied.

Syntax

IMSECH(complex_number)

• complex_number: A complex number expressed in the form “x+yi”, where “x” is the real part and “y” is the imaginary part. For example, 2+3i.

Example #1

=IMSECH("2+3i")

This function call calculates the hyperbolic secant of the complex number 2+3i. As a result, it yields approximately 0.137 + 0.936i.

Example #2

=IMSECH("0+1i")

Here, IMSECH returns the hyperbolic secant of the complex number 0+i, which results in approximately 1.086 + 0i.

Example #3

=IMSECH("-1-1i")

This function call returns the hyperbolic secant of the complex number -1-1i. The result is approximately 0.174 + 0.595i.

Error handling

• VALUE!: This error occurs if the input is not a valid complex number format.
• NUM!: This indicates that the function’s calculations had issues, possibly due to an invalid input leading to an undefined result.

Conclusion

In summary, the IMSECH function serves as a valuable resource for those dealing with complex mathematics in Google Sheets. By simplifying the process of calculating the hyperbolic secant, it provides users with efficient and accurate results that can enhance analysis and decision-making in various applications.