The Excel IMLOG10 Function

Related Function:
IMLN Function
Common Logarithm of a Complex Number

The common (base 10) logarithm of a complex number is calculated by the equation: See Wikipedia for further information on complex numbers.

Function Description

The Excel Imlog10 function returns the common (base 10) logarithm of a supplied complex number.

The syntax of the function is:

IMLOG10( inumber )

where the inumber argument is the complex number that you want to find the base 10 logarithm of.

Complex Numbers in Excel

Note that complex numbers are simply stored as text in Excel. When a text string in the format "a+bi" or "a+bj" is supplied to one of Excel's built-in complex number functions, this is interpreted as a complex number.

Also the complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.

Therefore, the inumber argument can be supplied to the Excel Imlog10 function as any of the following:

• A simple number;
• A complex number encased in quotation marks - e.g. "5+3i";
• A reference to a cell containing a complex number or a numeric value;
• A value returned from another Excel function or formula.

Imlog10 Function Examples

The spreadsheets below show four examples of the Imlog10 function:

Formulas:
AB
1 =IMLOG10( 2 )
2 =IMLOG10( "1-2i" )
32.5-i=IMLOG10( A3 )
4 =IMLOG10( COMPLEX( 1, -1 ) )
Results:
AB
1 0.301029995663981
2 0.349485002168009-0.480828578784234i
32.5-i0.349485002168009-0.201359598136687i
4 0.150514997831991-0.34109408846046i

Note that, in the above example spreadsheet:

• The integer 2, used in cell B1, is equal to the complex number 2+0i;
• The example in cell B4 uses the Excel Complex Function to create the complex number 1-i.

Further details and examples of the Excel Imlog10 function are provided on the Microsoft Office website

Imlog10 Function Errors

If you get an error from the Excel Imlog10 Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if the supplied inumber argument is not recognised as a complex number. #VALUE! - Occurs if the supplied inumber argument is a logical value.