The IMABS function returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.

Syntax

=IMABS(inumber)

Arguments

Argument Description
inumber A complex number for which you want the absolute value. The inumber argument can be supplied to the IMABS function as either:

  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 function or formula

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.

Examples

  A B C
1 Formula Result Notes
2 =IMABS(“5+12i”) 13 Absolute value of 5+12i
3 =IMABS(6) 6  
4 =IMABS(“3i”) 3  
5 =IMABS(COMPLEX(4,1)) 4.123105626  

Common Function Error(s)

Problem What went wrong
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number
#NAME? Occurs when Analysis ToolPak add-in is not enabled

The absolute value (the modulus) of a complex number is calculated as the square root of the sum of the squares of the real and imaginary coefficients, i.e. the modulus of the complex number, z = a + bi is:

    \[ \label{eq:imabs}|z|=\sqrt{a^2+b^2}\]

Further information on Complex Numbers can be found on the Wikipedia Complex Numbers Page.