The IMLOG function in Google Sheets is a powerful tool for performing logarithmic calculations on complex numbers. It allows users to compute logarithms with a specified base, making it particularly useful in fields such as engineering, mathematics, and data analysis where complex numbers are frequently encountered.

Syntax

IMLOG(complex_number, base)

• complex_number: The complex number for which you want to calculate the logarithm, represented in the form “a + bi”.
• base: The base of the logarithm you wish to use; must be a positive number except for 1.

Example #1

=IMLOG("3 + 4i", 10)

This function calculates the logarithm of the complex number 3 + 4i in base 10. For this specific example, the result would be approximately 0.613 + 0.927i.

Example #2

=IMLOG("1 + 2i", 2)

This computes the logarithm of the complex number 1 + 2i in base 2. The output for this function call would be around 0.568 + 1.107i.

Example #3

=IMLOG("-1 - i", 3)

This function evaluates the logarithm for the complex number -1 – i in base 3. The result would roughly yield -0.682 + 2.356i.

Error handling

• NUM! This error occurs when the specified base is less than or equal to zero or is equal to 1.
• VALUE! This indicates that the complex number is not in the correct format; it should be in the form “a + bi”.

Conclusion

The IMLOG function is an essential tool for working with complex numbers and performing logarithmic calculations in Google Sheets. By understanding its syntax and how to handle potential errors, users can leverage this function effectively for various applications in mathematics and science.