# The Excel IMARGUMENT Function

## Function Description

The Excel IMARGUMENT function returns the argument θ, (an angle expressed in radians), of a supplied complex number.

θ is the angle that satisfies the following equation:

The syntax of the Imargument function is:

IMARGUMENT( inumber )

where the inumber argument is a complex number.

## Excel Imargument Function Examples

In the spreadsheet below, the Excel Imargument function is used find the angle θ, of five different complex numbers.

Formulas:
A B
1 5+2i =IMARGUMENT( A1 )
2   =IMARGUMENT( "2-i" )
3   =IMARGUMENT( 6 )
4   =IMARGUMENT( "3i" )
5   =IMARGUMENT( COMPLEX( 4, 1 ) )
Results:
A B
1 5+2i 0.380506377
2   -0.463647609
3   0
4   1.570796327
5   0.244978663

Note that, in the above example spreadsheet:

• The integer 6, used in cell B3, is equal to the complex number 6+0i;
• The example in cell B5 uses the Excel Complex Function to create the complex number 4+i.

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

## Imargument Function Errors

If you get an error from the Excel Imargument 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.