IMLN Google Sheet Formula

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IMLN Formula Syntax

=IMLN("3+4i")

Example Use Case

Calculating the natural logarithm of a complex number

Understanding the IMLN Formula

The IMLN function in Excel returns the natural logarithm of a complex number. It's an advanced mathematical tool for complex analysis—like reversing exponential operations, solving certain types of complex equations, or analyzing complex transformations.

IMLN("3+4i") returns the natural logarithm of the complex number "3+4i". It takes a complex number argument in the form of text ("x+yi" or "x+yj"), calculating ln(z) = ln|z| + i×Arg(z)—valuable for applications in physics, engineering, or mathematics involving complex logarithms.

Why Use IMLN?

IMLN enables complex logarithmic calculations—think control theory or complex variable analysis. Its proper implementation of the complex natural logarithm makes it essential for advanced mathematical operations where the standard LN function is insufficient due to the complex domain.

Example with Sample Data

Complex Number	Formula	Result
"3+4i"	=IMLN("3+4i")	1.6094379124341+0.9272952180016i
"1+i"	=IMLN("1+i")	0.3465735902799+0.7853981633974i
"5"	=IMLN("5")	1.6094379124341

IMLN computes complex logarithms: ln(3+4i) approximately equals 1.61+0.93i. The result consists of the natural log of the magnitude (ln(5) ≈ 1.61) and the argument of the complex number (arctan(4/3) ≈ 0.93). For real positive numbers, it works just like the regular LN function. It's a complex logarithm calculator.