The IMARGUMENT function in Google Sheets is a valuable tool for users working with complex numbers. This function enables you to extract the angle or argument of a given complex number, returning the result in radians. Understanding the angle of a complex number is essential in various mathematical and engineering applications, particularly in fields such as signal processing and control systems.

Syntax

IMARGUMENT(complex_number)

• complex_number: This is the complex number for which you want to find the angle. It can be provided either as a string (e.g., “3+4i”) or as a reference to a cell containing the complex number.

Example #1

IMARGUMENT("3+4i")

This function call computes the angle of the complex number 3 + 4i. The result will be approximately 0.927 radians.

Example #2

IMARGUMENT(A1)

Assuming cell A1 contains the complex number “1+2i”, this function retrieves the angle of that complex number, yielding a result of approximately 1.107 radians.

Example #3

IMARGUMENT("-1-1i")

This example calculates the angle for the complex number -1 – 1i. The resulting angle will be approximately -2.356 radians, reflecting the position in the complex plane.

Error handling

• VALUE!: This error occurs if the input provided is not recognized as a valid complex number. Ensure that the input is correctly formatted (e.g., using ‘a+bi’ format).
• NUM!: This error may appear if the function’s argument is a number outside the acceptable range for a complex number. Verify that the input is a valid complex string or cell reference.

Conclusion

In summary, the IMARGUMENT function is an essential tool for calculating the angle of complex numbers in radians within Google Sheets. By employing the function correctly and understanding its syntax, users can effectively analyze complex numbers for various applications in mathematics and engineering.