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# The Excel IMAGINARY Function

Complex Numbers

Within the world of complex numbers, the 'imaginary' value, *i* is used to represent the square root of -1.

A Complex Number is composed of a real number combined with an imaginary number.

E.g. The complex number, *z*, is written as

*z* = 5 + 2*i*

Related Function:

IMREAL Function## Basic Description

The Excel IMAGINARY function returns the imaginary coefficient of a supplied complex number.

I.e. for the complex number **a + bi**, the Excel Imaginary function returns the value **b**.

The syntax of the function is:

IMAGINARY( inumber )

where the inumber argument is a complex number.

### 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 Imaginary 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.

## Excel Imaginary Function Examples

In the example spreadsheet below, the Excel Imaginary function is used find the imaginary coefficient of five different complex numbers.

Formulas: | A | B |
---|
1 | 5+2i | =IMAGINARY( A1 ) |
---|
2 | | =IMAGINARY( "2-i" ) |
---|
3 | | =IMAGINARY( 6 ) |
---|
4 | | =IMAGINARY( "3i" ) |
---|
5 | | =IMAGINARY( COMPLEX( 4, 1 ) ) |
---|
| Results: |

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 Imaginary function are provided on the Microsoft Office website.

## Imaginary Function Errors

If you get an error from the Excel Imaginary 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. |