# Documentation/Calc Functions/IMLOG10

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## Function name:

IMLOG10

## Category:

Add-in

## Summary:

Calculates the logarithm to the base 10 or common logarithm of a complex number.

## Syntax:

IMLOG10(**ComplexNumber**)

## Returns:

Returns a text string giving the complex number that is the common logarithm of the complex number passed as argument.

## 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 common 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 IMLOG10 as a number rather than a string. - If both real and imaginary parts of
**ComplexNumber**are 0, IMLOG10 reports an invalid argument error (Err:502). - If
**ComplexNumber**is not a valid complex number, IMLOG10 reports an invalid argument error (Err:502).

## Additional details:

### Details specific to IMLOG10 function

For a complex number of the form *a+bi*, the common logarithm is given by the following equation:

- IMLOG10(“a+bi”) = 0.434294481903251828 * IMLN(“a+bi”)

The value 0.434294481903251828 is the common logarithm of the mathematical constant *e*, which is known as Euler's number and has a value of approximately 2.71828.

### General information about Calc's handling of complex numbers

- A complex number is
**a number that can be expressed in the form**, where*a*+*bi**a*and*b*are real numbers and*i*is a symbol for the imaginary unit, such that*i*^{2}=−1.*a*is known as the real part of the complex number and*b*is known as its imaginary part.

- In some disciplines using
*i*to indicate the imaginary unit may be undesirable and, in such cases,**the symbol**. The functions provided by Calc to process complex numbers can use either*j*may be used instead*i*or*j*.

- For additional
**general background information**, visit Wikipedia’s Complex number page.

- Within Calc,
**a complex number is represented as a string expression**of the form "a+bi" or "a+bj", where*a*and*b*are real numbers. If the complex number happens to be a real number (*b*=0), then it can be represented as either a string expression or a numeric value. Complex number string expressions should not contain any space characters. Examples of valid Calc complex numbers include "2", -6, "2+3i", "3j", "12.34+56.78i", and "1e+23-1e-22j". Calc would not recognize the strings "1+j2", "i+1", and "i+j" as valid complex numbers.

- The representation of the complex numbers in strings can have
**up to 15 significant digits**and scientific style is automatically used if needed (visit Wikipedia’s Scientific notation page for more information). The decimal delimiter in complex number string expressions is always a dot, irrespective of locale setting.

## Examples:

Formula | Description | Returns |
---|---|---|

=IMLOG10("1.2-3.4j") | Here the function calculates the common logarithm of a complex number that has non-zero real and imaginary parts. | 0.556971676153418-0.534835266713002j |

=IMLOG10("-i") | Here the function calculates the common logarithm of a complex number that has no real part. The result has no real part. | -0.682188176920921i |

=IMLOG10(-1) | Here the function calculates the common logarithm of a complex number that has no imaginary part. The result has no real part. | 1.36437635384184i |

=IMLOG10("-1e20-i") | Here the function calculates the common logarithm of a complex number that has non-zero real and imaginary parts. | 20-1.36437635384184i |

=IMLOG10(F1) where cell F1 contains the complex number 2-3j. | Here the function calculates the common logarithm of a complex number that is entered in a cell. | 0.556971676153418-0.426821890855467j |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

IMLOG10