Mehedi Hasan Shimul
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.
- 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.
- 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.
- 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.
- 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.
- 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.
