The IMLN function in Google Sheets is a powerful tool that computes the natural logarithm of complex numbers using the base of Euler’s number (approximately 2.71828). With this function, users can easily analyze complex data in fields such as engineering, physics, and advanced mathematics.

Syntax

IMLN(complex_number)

complex_number: A required parameter representing the complex number for which the logarithm is to be computed. It can be in the format of a string such as "a + bi" or can be provided through the real and imaginary parts.

Example #1

IMLN("3+4i")

Calculates the natural logarithm of the complex number 3 + 4i. The result is approximately 1.223775 + 0.927295i, which gives insight into the magnitude and direction of the complex number in the complex plane.

Example #2

IMLN(1)

Computes the logarithm of the complex number 1. The result is 0 + 0i, demonstrating that the natural logarithm of one is zero, regardless of whether the input is considered in the complex plane or real number line.

Example #3

IMLN("-2 + 0i")

Evalues the logarithm of the complex number -2 + 0i. The result is approximately 0.693147 – 3.141593i, showing the impact of the negative number on the logarithmic transformation in complex analysis.

Error handling

• VALUE!: Indicates that the input provided is not in a valid format. Ensure that the complex number is formatted correctly, such as “a + bi”.
• NUM!: This error signifies that the complex number is out of the calculation range. Check the values supplied to ensure they are numerical.
• REF!: Implies a reference issue, typically occurring when the referenced cell or data is missing. Confirm all references in your formula are correctly linked.

Conclusion

The IMLN function is invaluable for those working with complex numbers, providing essential insights through the natural logarithm. By utilizing this function, users can enhance their data analysis capabilities in various advanced applications, reinforcing its utility across mathematical and engineering disciplines.