The IMCONJUGATE function in Google Sheets is designed to return the complex conjugate of a given complex number. This function plays a crucial role in various mathematical computations, particularly in fields involving electrical engineering, signal processing, and complex number analysis.

Syntax

IMCONJUGATE(complex_number)

• complex_number: This parameter refers to the complex number you wish to find the conjugate for, expressed in a standard format such as “a + bi” where “a” is the real part and “b” is the imaginary part.

Example #1

=IMCONJUGATE("3 + 4i")

This function will return the conjugate of the complex number 3 + 4i, giving a result of 3 – 4i.

Example #2

=IMCONJUGATE("-2 - 5i")

This call will yield the complex conjugate of -2 – 5i, resulting in -2 + 5i.

Example #3

=IMCONJUGATE("1 + 0i")

In this instance, the function will return the conjugate of the purely real complex number 1, which remains 1 + 0i.

Error handling

• VALUE!: This error occurs when the input is not a valid complex number format. Ensure that the complex number is entered correctly, using “a + bi” notation.
• NUM!: This error indicates that the function is unable to handle the number provided. It may happen if the number exceeds the acceptable limits for complex numbers.

Conclusion

The IMCONJUGATE function is an essential tool for those dealing with complex numbers in Google Sheets. By providing a straightforward way to calculate the conjugate, it facilitates a variety of mathematical and engineering applications. Understanding how to use this function effectively can greatly enhance your ability to manipulate complex data and perform advanced calculations.