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Excel IMLN Function

The IMLN function returns the natural logarithm of a given complex number in x + yi or x + yj text format. The natural logarithm is the log value with base e (Euler's number), where e is approximately equal to 2.71828.

imln function 1




  • inumber (required): A complex number for which to get the natural logarithm.

Return Value

The IMLN function returns a complex number as text.

Function Notes

  • inumber can be supplied as any of the following:
    • A real number whose imaginary part is 0, e.g., 1 is a complex number 1+0i; Or a purely imaginary number whose real part is 0, e.g., i is a complex number 0 + 1i;
    • A cell reference that refers to a complex number;
    • A complex number enclosed in double quotation marks.
  • inumber can be returned by the COMPLEX function which converts real and imaginary coefficients into a complex number.
  • IMLN will return the #NUM! error if inumber is not recognized as a complex number that has lowercase i or j (iota).
  • IMLN will return the #VALUE! error if inumber is a logical value.
  • The natural logarithm of a complex number is:
    imln function equation


To get the natural logarithm of the complex numbers listed in the below table, please copy or enter the formula below in the top cell, press Enter to get the result, and then drag the fill handle (at the lower right corner of the result cell) down to apply the formula to below cells.


imln function 2

Also, you can type the actual complex number in the formula as shown below. Make sure the complex number is enclosed with double quotes:


Related functions

Excel COMPLEX Function

The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Excel EXP Function

The EXP function returns the result of the constant e raised to the nth power, where e, the base of the natural logarithm, equals 2.71828183 approximately.

Excel IMLOG2 Function

The IMLOG2 function returns the base-2 logarithm of a given complex number in x + yi or x + yj text format.

Excel IMLOG10 Function

The IMLOG10 function returns the common (base 10) logarithm of a given complex number in x + yi or x + yj text format.

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