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IMLN Function

Excel 2007+

Summary

The Excel IMLN function calculates the natural logarithm of a complex number provided in x+yi or x+yj text format. This engineering function returns results as complex numbers, making it essential for advanced mathematical computations involving imaginary values.

Syntax

IMLN(inumber)

Parameters

Parameter	Type	Required	Description
inumber	`Complex Number`	Yes	A complex number entered as text in x+yi or x+yj format

Using the IMLN Function

IMLN is designed for complex number mathematics, particularly useful in electrical engineering, physics, and advanced analytics where natural logarithms of non-real numbers are required. Combine it with COMPLEX function to create inputs from separate real/imaginary components.

Common IMLN Examples

Basic Complex Logarithm

=IMLN("3+4i")

Calculates natural logarithm of 3+4i, returning approximately 1.6094+0.9273i

Using COMPLEX with IMLN

=IMLN(COMPLEX(3,4))

Converts real (3) and imaginary (4) parts to complex number, then finds natural log.

Frequently Asked Questions

Complex numbers in 'x+yi' or 'x+yj' text format, or created via COMPLEX function.

A complex number representing the natural logarithm in x+yi format.

Common Errors and Solutions

#NUM! error

Cause: Invalid complex number format

Solution: Use proper x+yi format or COMPLEX function

#VALUE! error

Cause: Non-complex number input

Solution: Ensure input is valid complex number text

Notes

Formula: Log(z) = ln|z| + i·Arg(z) where z is complex
Use COMPLEX(real_num, i_num) to build inputs
Related functions: IMLOG2, IMLOG10 for different bases
Excel 2007+ including Microsoft 365

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+