# The Excel IMSUM Function

When adding complex numbers, the real and imaginary coefficients are added separately.

I.e. the equation to find the sum of two complex numbers a+bi and c+di is:

(a+bi) + (c+di) = (a+c) + (b+d)i

Complex Numbers are explained in detail on the Wikipedia Complex Numbers Page.

Related Function:
IMSUB Function

## Function Description

The Excel Imsum function calculates the sum of two or more complex numbers.

The syntax of the function is:

IMSUM( inumber1, inumber2, ... )

where the inumber arguments are between 2 and 255 Complex Numbers.

### 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 arguments can be supplied to the Excel Imsum function as either:

• Simple numbers;
• Complex numbers encased in quotation marks - e.g. "5+3i";
• References to cells containing complex numbers or numeric values;
• Values returned from other Excel functions or formulas.

## Imsum Function Examples

The spreadsheets below show three examples of the Excel Imsum function:

Formulas:
AB
11-i=IMSUM( A1, A2 )
25+10i=IMSUM( "1-i", "5+10i", 2 )
3 =IMSUM( COMPLEX( 5, 2 ), COMPLEX( 0, 1 ) )
Results:
AB
11-i6+9i
25+10i8+9i
3 5+3i

Note that, in the above example spreadsheet:

• The integer 2, used in cell B2, is equal to the complex number 2+0i;
• The example in cell B3 uses the Excel Complex Function to create the complex numbers 5+2i and i.

Further details of the Excel Imsum function are provided on the Microsoft Office website.

## Imsum Function Errors

If you get an error from your Excel Imsum function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if any of the supplied inumber arguments are not recognised as complex numbers. #VALUE! - Occurs if any of the supplied inumber arguments are logical values.