# How to Add Complex Numbers in Excel (With Easy Steps)

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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.

## 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.

• 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.

• Firstly, write the following formula in Cell B5 to include a complex number there.
`=COMPLEX(10,20)`
• Simultaneously, hit Enter.

In the formula, we included 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.

In the formula, cell reference 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.

In the formula, the 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.

In the formula, 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.

In the formula, the 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.

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Mehedi Hasan Shimul

Hi! I am Mehedi Hasan Shimul. As I am an Engineer solving different problems with the help of Excel amuses me. I write Excel related different problem solving articles here. Hope it will help you.

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