The IMCOTH function in Google Sheets is a powerful tool for mathematicians and statisticians who need to work with complex numbers. This function returns the hyperbolic cotangent of an input complex number, providing insights that are especially useful in fields like engineering and physics.

Syntax

IMCOTH(complex_number)

• complex_number: The complex number for which you want to calculate the hyperbolic cotangent. It should be in the form of “x+yi” or defined using the COMLEX function.

Example #1

=IMCOTH("2+3i")

This function will calculate the hyperbolic cotangent of the complex number 2 + 3i, resulting in approximately 0.00330 + 0.25327i.

Example #2

=IMCOTH(COMLEX(1,1))

Here, the function computes the hyperbolic cotangent of the complex number 1 + 1i. The result is about 0.50000 + 0.00000i, illustrating how the function handles complex inputs seamlessly.

Example #3

=IMCOTH("5+0i")

With this instance, the function determines the hyperbolic cotangent of the purely real number 5, which yields a result of approximately 0.00000 + 1.00000i, showcasing its versatility.

Error handling

• VALUE!: This error arises when the input is not recognized as a valid complex number. Ensure that the format is correct before retrying.
• NUM!: This error indicates that the function encountered a numerical problem while calculating the complex cotangent. Check the input values for any anomalies.
• N/A: This error occurs if no valid input has been provided. Make sure to input a complex number for the function to work properly.

Conclusion

The IMCOTH function is an invaluable asset for anyone who works with complex numbers in Google Sheets. By facilitating the calculation of the hyperbolic cotangent, it opens doors for deeper mathematical analysis and application, particularly in fields such as engineering and applied mathematics.