## How to use the IMREAL function

The IMREAL function calculates the real coefficient of a complex number in x + yi or x + yj text format.

The letter j is used in electrical engineering to distinguish between the imaginary value and the electric current.

### Table of Contents

## 1. IMREAL Function Syntax

IMREAL(*inumber*)

## 2. IMREAL Function Arguments

inumber |
Required. A complex number in x+yi or x+yj text format. |

## 3. IMREAL function example

The image above demonstrates a formula in cell C25 that calculates the real coefficient of a complex number specified in cell B25. Cell B25 contains "3+4i" which is a complex number constructed from a real and imaginary part.

The real part from cell B25 is extracted and displayed in cell C25, the imaginary part is shown in cell D25.

Formula in cell C25:

The image above also shows a chart of a complex plane, the real and imaginary numbers are coordinates. The real number is a dashed line representing the real number from "3+4i" to the real axis (x-axis).

### 3.1 Explaining formula

#### Step 1 - Populate arguments

IMREAL(*inumber*)

becomes

IMREAL(B3)

#### Step 2 - Evaluate the IMREAL function

IMREAL(B3)

becomes

IMREAL("3+4i")

and returns 3.

## 4. When to use the IMREAL function?

Use the IMREAL function when you want to

- add, subtract, multiply and divide complex numbers.
- calculate the modulus which is the distance from the origin to the point representing the complex number.
- graph complex numbers
- calculate the complex determinant of a 2x2 matrix

The links above points to articles explaining how to manually calculate these properties, however, Excel has functions so you don't need to calculate them manually:

IMSUM | IMSUB | IMPRODUCT | IMDIV | IMARGUMENT | IMABS

## 5. How to plot the real part of a complex number on a chart

The chart above demonstrates complex number "3+4i" on the complex plane. The y-axis is the imaginary axis and the x-axis is the real axis, the light blue line with an arrow represents the complex number from the origin (0,0) to (3,4).

The vertical dashed line displays the real number of the complex number "3+4i" on the real axis. The IMREAL function lets you extract the real number from a complex number, this is handy if you want to plot a complex number on chart.

A complex number number consists of a real number and an imaginary number, we need both these numbers to plot a complex number on a chart.

### 5.1 Calculate the real and imaginary numbers

To be able to plot the complex number on the complex plane we need to calculate the real and imaginary number separately. Cell B25 contains the complex number in rectangular form.

Formula in cell C25:

The IMREAL function extracts the real number from the complex number in cell B25.

Formula in cell D25:

The IMAGINARY function extracts the imaginary number from the complex number in cell B25.

To plot a line we must use coordinates from the origin (0,0), I have entered 0 zero in cells C24 and D24. The scatter chart we are soon going to create needs a blank row between the line coordinates in order to show two different lines not attached to each other.

The dashed line also needs two points on the chart in order to be displayed properly. It begins where the complex number ends (3,4) and ends at the real axis, the line is vertical meaning the end point must have an imaginary number of 0 (zero).

### 5.2 Insert a scatter chart

The following steps describe how to plot a complex number and the corresponding real number.

- Select cell range C24:D28.
- Go to tab "Insert" on the ribbon.
- Press with left mouse button on the "Insert Scatter (x,y) or Bubble chart" button.

- A popup menu appears, press with left mouse button on the "Scatter with straight lines".

A chart shows up on the worksheet, move the chart to its desired location.

Change the chart so it shows the complex number as a line with an ending arrow, the real number as a dashed line and so on. Here are detailed instructions:

How to plot theta Î¸ - Argand diagram

### Useful links

IMREAL function - Microsoft

Real and imaginary numbers

Imaginary numbers - Math is fun

### Functions in 'Engineering' category

The IMREAL function function is one of many functions in the 'Engineering' category.

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