In some branches of engineering and science, we often face operations with complex numbers. Fortunately, **Excel **has included different operations for complex numbers. It has many built-in functions to deal with complex numbers. So, we don’t need any extra software or application. In this article, we will show **how to add complex numbers in** **Excel**. In addition, we will also discuss other mathematical operations like subtraction, multiplication and division of complex numbers.

## Download Practice Workbook

You can download the practice workbook from here and practice yourself.

## What Are Complex Numbers?

In many cases, we can’t solve a mathematical problem with real numbers. Such as, we can’t find the square root of any negative number. For solving this sort of problem, imaginary numbers are introduced. For example, “**i**” is considered an imaginary number whose squire gives **-1 **as the value.

Complex numbers are numbers that consist of one real part and one imaginary part.

The format of a complex number: **a **+ **ib**, where “**a**” is the **real** **part** of the number and “**b**” is the **imaginary** **one**. Also, we can use “**j**” instead of “**i**” with the imaginary number part of the complex number.

## Step-by-Step Procedures to Add Complex Numbers in Excel

In this section, we will discuss the stepwise procedures to add complex numbers which is quite an easy task. We can do the addition by using **the IMSUM function **of **Excel**. For demonstration purposes, we have included **Set 1**, and **Set 2 **columns that contain two sets of complex numbers and column **Addition Result **for the sum result of those two sets of complex numbers.

### STEP 1: Enable Excel for Complex Number

The functions that deal with complex numbers are not included in the **Excel **workbook automatically. We have to enable **Excel **first to work with complex numbers. Let’s walk through the procedures.

- Firstly, go to the
**Developer**tab in the**Excel**ribbon. - Secondly, select
**Excel Add-ins**.

- Consecutively, an
**Add-ins**window will appear. In that window, put a mark on**Analysis Toolpak**and press**OK**.

- Finally, we will be able to include functions for complex numbers now.

### STEP 2: Insert Complex Numbers in Excel

In this step, we will show the way to include complex numbers in **Excel**. We will use **the COMPLEX function **of **Excel **for that. The **COMPLEX **function has been introduced in **Excel 2007 **and available for all versions after that. Let me show the **Syntax **and **Arguments **of this function.

**Syntax:**

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

**Arguments:**

**real_num:**It indicates the real part of the complex number. It is a required argument.**i_num:**This is the second required argument. It denotes the imaginary part of the complex number.**[suffix]:**This argument is optional. We can input**“i”**or “**j**”. If we don’t give anyone then**Excel**will include “**i**” with the imaginary part of the complex number by default.

Let’s jump to the procedures,

- Firstly, write the following formula in
**Cell B5**to include a complex number there.

`=COMPLEX(10,20)`

- Simultaneously, hit
**Enter**.

**10**and

**20**as the

**real_num**and

**i_num**arguments of the

**COMPLEX function**. We didn’t add

**[suffix]**argument. By default, it’ll be “

**i**”.

- In a similar manner, we should more complex numbers in
**Set 1**and**Set 2**for addition.

**Read More: ****How to Use IMAGINARY Function in Excel**

### STEP 3: Use IMSUM Function to Add Complex Numbers

Now, we will show how to add complex numbers from **Set 1 **with complex numbers from **Set 2 **and display the result in the **Addition Result **column. For doing the addition, we will use **the IMSUM function **of **Excel**. This function is also available in **Excel 2007 **and newer versions.

**Syntax:**

`=IMSUM(inumber1,[inumber 2],…)`

**Arguments:**

**inumber 1**: It is the required argument. It indicates the complex number**1**for addition.**inumber 2**: This is an optional argument that denotes the complex number**2**for addition.

This way the function can take up to **255 **complex numbers as arguments for addition.

Let’s walk through the procedures.

- Firstly, select
**Cell D5**where we want the result of addition and write the following formula there.

`=IMSUM(B5,C5)`

- Then, hit
**Enter**.

**B5**and

**C5**contains

**2**complex numbers which act as the arguments for the

**IMSUM**function. Also, the

**IMSUM**function adds the two complex numbers and shows the result.

- Later on, use the
**AutoFill**option of**Excel**to copy the formula in the following cells. - Finally, we will see the sum results of complex numbers from
**Set 1**and**Set 2**in**Addition Result**column.

## How to Subtract, Multiply and Divide Complex Numbers in Excel

Except for addition, we can also use different functions of **Excel **to subtract or multiply or divide complex numbers. In this section, we will discuss the procedures of all these three operations in **Excel**.

### Subtraction of Complex Numbers in Excel

For the subtraction of complex numbers, **Excel **has **the IMSUB function**. We will show how to use the function to get the subtraction value of two complex numbers. Let’s follow the steps given below.

- Firstly, input some complex numbers in
**Set 1**and**Set 2**as we did previously.

- Then, write the following formula in
**Cell D5**to get to subtract the complex number of**Cell C5**from the complex number of**Cell B5**.

`=IMSUB(B5,C5)`

- Then, press
**Enter**.

**IMSUB**function subtracts the complex number of

**Cell C5**from the complex number of

**Cell B5**.

- Afterward, use the
**Fill Handle**option of**Excel**to get the subtraction value for the rest complex numbers from**Set 1**and**Set 2**. - Finally, we will see all the subtraction results.

### Multiplication of Complex Numbers in Excel

Multiplication is also a common operation for complex numbers. We can do the multiplication of complex numbers in **Excel **using **the IMPRODUCT function**. Now, we will show the way to multiply complex numbers in **Excel**.

- Primarily, input some complex numbers in
**Set 1**and**Set 2**. We will multiply complex numbers from**Set 1**with complex numbers from**Set 2**.

- Then, write the following formula in
**Cell D5**.

`=IMPRODUCT(B5,C5)`

- Consecutively, hit
**Enter**and we will see the multiplication result in**Cell D5**.

**B5**and

**C5**are cells containing complex numbers. The

**IMPRODUCT**function multiplies the complex numbers as they are in the argument.

**Note:**We can add up to

**255**complex numbers as arguments of the

**IMPRODUCT**function. The function will multiply them all.

- Later on, use the
**Fill Handle**option of**Excel**to see the multiplication results in the following cells. - Finally, we will see all the multiplication results.

### Division of Complex Numbers in Excel

Also, we can divide complex numbers in **Excel**. For that, **Excel **has** the** **IMDIV function**. In this section, we will discuss the way to divide complex numbers in **Excel**. Follow the given steps.

- Firstly, include some complex numbers in
**Set 1**and**Set 2**as we did before.

- Then, write the following formula in
**Cell D5**.

`=IMDIV(B5,C5)`

- Simultaneously, press
**Enter**and we will see the division result in**Cell D5**.

**IMDIV**function divides the complex number from

**Cell B5**by the complex number from

**Cell C5**as they are in the argument.

- Further, use the
**Fill Handle**of**Excel**to copy the formula in the cells below. - Finally, we will see the results in all the cells of
**Division Result**.

## Things to Remember

In this article, we have used different functions of **Excel **that deal with complex numbers. We can insert those functions from the **Excel **ribbon following the given steps.

- Firstly, open the
**Formulas**tab. - Afterward, select
**More Functions**>**Engineering**. - Finally, select the desired function from the appeared list.

## Conclusion

Complex numbers are widely used to solve different engineering and mathematical problems. In this article, we have shown the step-by-step procedures to **add complex numbers in** **Excel**. In addition, we have also shown the methods to subtract, multiply and divide complex numbers in **Excel**. Hopefully, this article will help you. If you have any queries or suggestions, please leave a comment. Visit our **ExcelDemy Website **for similar articles regarding **Excel**.