The IMSINH function in Google Sheets is designed to compute the hyperbolic sine of a complex number. It’s particularly useful for advanced mathematical calculations involving complex number theory and can be a vital asset for students and professionals alike.

Syntax

IMSINH(complex_number)

• complex_number: The complex number for which the hyperbolic sine is calculated, formatted as “x+yi” where x is the real part and y is the imaginary part.

Example #1

IMSINH("3+4i")

This call computes the hyperbolic sine of the complex number 3+4i. The expected result is: 3.893658 – 27.289917i.

Example #2

IMSINH("1+2i")

In this case, the function calculates the hyperbolic sine of 1+2i. The result is approximately: 1.403119 – 2.261945i.

Example #3

IMSINH("0+0i")

Here, the function evaluates the hyperbolic sine of the complex number 0+0i, yielding a result of: 0.

Error handling

• VALUE! This error occurs if the input is not recognized as a valid complex number format.
• NUM! Indicates that the function cannot process the specific input due to invalid numerical values.

Conclusion

The IMSINH function is a powerful tool in Google Sheets for performing calculations involving the hyperbolic sine of complex numbers. Understanding its syntax and potential errors can significantly enhance the user’s ability to work with complex mathematical operations efficiently.