Documentation/Calc Functions/IMLN

Function name:
IMLN

Category:
Add-in

Summary:
Calculates the logarithm to the base e or natural logarithm of a complex number. e is a mathematical constant known as Euler's number, which has a value of approximately 2.71828.

Syntax:
IMLN(ComplexNumber)

Returns:
Returns a text string giving the complex number that is the principal natural logarithm of the complex number passed as argument. The imaginary part of the principal natural logarithm lies in the range -&pi; < x ≤ &pi;.

Arguments:
ComplexNumber is a string (in quotation marks) representing a complex number in the form a+bi or a+bj, or a reference to a cell containing that string, which is the complex number for which the natural logarithm is to be calculated. a and b are real numbers.


 * If ComplexNumber does not have an imaginary part (b equal to 0), the real part can be passed to IMLN as a number rather than a string.
 * If both real and imaginary parts of ComplexNumber are 0, IMLN reports an invalid argument error (Err:502).
 * If ComplexNumber is not a valid complex number, IMLN reports an invalid argument error (Err:502).

Details specific to IMLN function
For a complex number of the form a+bi, the natural logarithm is given by the following equation: IMLN uses an alternative formulation for the imaginary part based on an equivalent inverse cosine function call instead of the inverse tangent function call, along with a necessary check to ensure that the correct sign is applied to the imaginary part of the result.

For more information, visit Wikipedia’s Complex logarithm page.

Related LibreOffice functions:
IMEXP

IMLOG10

IMLOG2

IMPOWER

IMSQRT

ODF standard:
Section 6.8.14, part 2

Equivalent Excel functions:
IMLN