# COMPLEX function

This article describes the formula syntax and usage of the COMPLEX function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Excel.

## Description

Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.

## Syntax

`COMPLEX(real_num, i_num, [suffix])`

The COMPLEX function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• Real_num    Required. The real coefficient of the complex number.
• I_num    Required. The imaginary coefficient of the complex number.
• Suffix    Optional. The suffix for the imaginary component of the complex number. If omitted, suffix is assumed to be "i".

Note   All complex number functions accept "i" and "j" for suffix, but neither "I" nor "J". Using uppercase results in the #VALUE! error value. All functions that accept two or more complex numbers require that all suffixes match.

## Remarks

• If real_num is nonnumeric, COMPLEX returns the #VALUE! error value.
• If i_num is nonnumeric, COMPLEX returns the #VALUE! error value.
• If suffix is neither "i" nor "j", COMPLEX returns the #VALUE! error value.

## Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

A B
Formula Description (Result)
=COMPLEX(3,4) Complex number with 3 and 4 as the real and imaginary coefficients (3 + 4i)
=COMPLEX(3,4,"j") Complex number with 3 and 4 as the real and imaginary coefficients, and j as the suffix (3 + 4j)
=COMPLEX(0,1) Complex number with 0 and 1 as the real and imaginary coefficients (i)
=COMPLEX(1,0) Complex number with 1 and 0 as the real and imaginary coefficients (1)

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses