The IMEXP function in Google Sheets is a powerful tool that enables users to compute Euler’s number, denoted as e (approximately 2.718), raised to a complex number power. This function is particularly useful in advanced mathematical computations, physics, engineering, and other fields that utilize complex numbers.

Syntax

IMEXP(complex_number)

• complex_number: This parameter represents the complex number for which you wish to calculate e raised to its power. It can be entered in the form “a + bi”, where ‘a’ is the real part and ‘b’ is the imaginary part.

Example #1

=IMEXP("2 + 3i")

This function calculates Euler’s number raised to the power of the complex number 2 + 3i. The result would be approximately -0.1394 + 0.4119i.

Example #2

=IMEXP("0 + 1i")

Here, the function computes e raised to i (the imaginary unit). The result will be approximately 0 + 1i, equivalent to the circular function cos(1) + isin(1), approximately 0.5403 + 0.8415i.

Example #3

=IMEXP("-1 + 0i")

In this example, the function calculates e raised to the power of -1, which results in approximately 0.3679 + 0i, a representation of the decay factor in various mathematical models.

Error handling

• NUM!: This error occurs if the input is not a valid complex number.
• VALUE!: This error indicates that the input is in an incorrect format, such as a missing component in the complex number representation.

Conclusion

The IMEXP function is an essential utility for anyone working with complex numbers in Google Sheets. By leveraging this function, users can easily and accurately perform calculations involving Euler’s number raised to complex powers, enhancing their analytical capabilities in various fields of study.