Imaginary numbers are often used for mathematical and scientific analysis. In this article, we will show you how you can use the Excel **IMAGINARY **Function. With the help of this function, you can find the coefficient of the imaginary portion. You will also get a complete idea about inserting complex numbers, extracting real coefficients, and some common and most-used complex number calculations.

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## Download Practice Workbook

You can download and practice this workbook.

## Introduction to IMAGINARY Function

**Summary**

The **IMAGINARY **function extracts the imaginary coefficient from the corresponding complex number in Excel.

**Syntax**

The syntax for the formula is:

`=IMAGINARY(inumber)`

**Argument**

Argument |
Required/Optional |
Value |
---|---|---|

inumber |
Required | The complex number from which you want to get the imaginary coefficient |

**Output**

Returns the imaginary coefficient of a complex number.

**Available Versions**

The **IMAGINARY** function is available in all versions of Excel.

## Insert Complex Number with Real and Imaginary Part in Excel

Let’s say, we have a dataset of some real and imaginary coefficients from which we want to form complex numbers.

Let’s check the procedure of inserting complex numbers first.

We can Insert Imaginary numbers in Excel using the **COMPLEX function**.

➤ Write the Following equation in the desired cell and

`=COMPLEX(1,2)`

Here,

**1**:- Real Coefficient**2**:- Imaginary Coefficient

thus, we get the Imaginary form.

➤ Then press **ENTER** and the cell will show you the complex number by combining the real and imaginary portions with a suffix “**i**”.

But there is a drawback to this method. Each time you want to insert a complex number, you need to input the real and the imaginary portion each and every time. However, you can apply this procedure when you have to get the complex number directly.

There is another way also available if you have a list of real and imaginary portions. You can use the cell reference. Here, we have lists of real and imaginary portions.

You just have to use the cell reference of the real and imaginary part.

➤ So, write the following Formula in the selected cell.

`=COMPLEX(B5,C5)`

Here,

**B5**:- Real Coefficient**C5**:- Imaginary Coefficient

➤ Now, press **ENTER **to let the cell show the result.

➤ Next, use the **Fill Handle **tool to **Autofill **the formula for the cells situated down to that cell.

➤ Hence, you will get the complex numbers formed of your inserted real and imaginary part.

## Common Uses of IMAGINARY Function in Excel.

This **IMAGINARY** function takes a Complex number and returns its Imaginary Coefficient. In this section, we will see how the imaginary function can be used in Excel. I will discuss 3 examples of using **IMAGINARY** function with proper illustrations here.

### 1. Extract Imaginary Coefficient Directly with Imaginary Function

We have taken some Imaginary Numbers in **Column B**.

And, we want to extract the Imaginary coefficient in **Column C**.

➤ Now, write the following formula in **C5** and press** ENTER**.

`=IMAGINARY("1+2i")`

Here, **“1+2i”** is the Complex Number

*Note**: When you wrap a text with an inverted comma assigned in the*

**IMAGINARY**function, it recognizes the text as a complex number.➤ Then, press **ENTER **and the cell will return you the imaginary coefficient of the assigned complex number.

➤ Each time you assign an individual complex number as the argument of the **IMAGINARY **function, you will get the corresponding imaginary coefficient from it.

Thus, we get all the imaginary coefficients for the corresponding imaginary numbers.

**Read More: ****How to Use COMPLEX Function in Excel (2 Practical Examples)**

### 2. Use Cell Reference in IMAGINARY Function

If you don’t want to use the **Inverted Comma** in the **IMAGINARY **function, you can use the cell reference. There is an extra advantage of using cell references. You don’t need to apply the formula every time like **Method 1 **here.

➤ First, just select a cell and type the following formula in that cell.

`=IMAGINARY(B5)`

Here,

**B5**:- Complex Number

➤ Now, press **ENTER **to show the result.

➤ Next, drag the formula down to copy it to the other cells. It will **Autofill **the formula for other cells.

➤ As a result, you will get the imaginary coefficient for all the complex numbers.

### 3. COMPLEX Function Nested in IMAGINARY Function in Excel

We have a list of some real numbers and some imaginary numbers (with the suffix “**i**”). We have learned how to** insert complex number with real and imaginary part** in Excel.

Now, we will see how we can use the **IMAGINARY **function nested with the **COMPLEX **function to get the imaginary coefficient from it.

➤ Here, type the following formula in cell **D5**.

`=IMAGINARY(COMPLEX(1,2))`

Here,

**1**:- Real Part**2**:- Imaginary Part

➤ Then, press **ENTER**, The **COMPLEX **function will return the complex number and so, the **IMAGINARY **function will extract the imaginary coefficient from it.

➤ Apply individual formulas each time to get the acquainted result.

## Extracting Real Coefficient from Imaginary Number with IMREAL Function

We have seen the use of the **IMAGINARY **function to extract the imaginary coefficient. But for real part, you have to use the **IMREAL **function.

This **IMREAL** function returns the real coefficient of an imaginary number.

We have taken the same imaginary numbers as previously used.

➤ Write the following formula in **C5** and press **ENTER**.

`=IMREAL(B5)`

Here,

**B5**:- Complex Number

So, we get the real coefficient for the first imaginary number.

➤ Now, **Hold** and **Drag** the **C5** cell downward.

And, we have all the real coefficients for all imaginary numbers.

## Practice Section

Here, we are providing you a practice section where you can practice yourself.

## Things to Remember

- While applying the complex number directly into the
**IMAGINARY**function, don’t forget to use the**Inverted****Comma**. Otherwise the function try to correct the formula and return**0**always. - If the complex number is used as cell reference, then there is no need to put
**Inverted Comma**.

## Conclusion

So, we learned how to use the **IMAGINARY **function in Excel. We hope you find the content of this article useful. If there are any queries or suggestions regarding any of these procedures, feel free to leave them in the comment section.