How to use the IMSUB function

Author: Oscar Cronquist Article last updated on June 05, 2023

IMSUB function4

What is the IMSUB function?

The IMSUB function calculates the difference between two complex numbers 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.

IMSUB Function Syntax
IMSUB Function arguments
IMSUB function example
How to calculate the difference between two complex numbers in rectangular form?
How to graph the difference between two complex numbers?
How to calculate the distance between two complex numbers?
Get Excel *.xlsx file

1. IMSUB Function Syntax

IMSUB(inumber1, inumber2)

2. IMSUB Function Arguments

inumber1	Required. A complex number in x+yi or x+yj text format.
inumber2	Required. A complex number in x+yi or x+yj text format.

3. IMSUB function example - rectangular form

How to use the IMSUB function

The image above demonstrates the IMSUB function in cell F3 that calculates the difference between two complex numbers specified in cells C3 and D3.

Formula in cell F3:

=IMSUB(C3, D3)

3.1 Explaining formula

Step 1 - Populate arguments

IMSUB(inumber1, inumber2)

becomes

IMSUB(C3, D3)

Step 2 - Evaluate the IMSUB function

IMSUB(C3, D3)

becomes

IMSUB("-2+2i","2-4i")

and returns

-4+6i

4. How to calculate the difference between two complex numbers in rectangular form?

How to use the IMSUB function

This example demonstrates how Excel calculates in detail the difference between two complex numbers in rectangular form.

C₁ is the first complex number specified in cell C3, C₂ is the second complex number specified in cell D3.

C₁ = x + yi

C₂ = z + wi

To calculate the difference between two complex numbers we need to find the difference between the real numbers and the imaginary numbers separately.

C₁- C₂ = (x + yi) - (z + wi) = (x - z) + (y - w)i

C₁ = -2+2i

C₂ = 2-4i

C₁- C₂ = (-2 + 2i) - (2 - 4i) = ((-2) -2) + (2 - (-4))i = -4+6i

5. How to graph the difference between two complex numbers?

IMSUB function chart the difference4

The image above demonstrates a scatter chart that shows two different complex numbers and their difference, in total three different complex values.

Complex numbers in rectangular form a+bi have real and imaginary values which are positive, negative or zero, this makes it possible to use a chart with two dimensions x and y.

The imaginary values on the vertical axis (y) and the real values on the horizontal axis (x).

C₁ = -2+2i (light blue)

C₂ = 2-4i (green)

C₁- C₂ = -4+6i (dark blue)

Subtracting a complex number means that it points the opposite way with the same distance (green). The dark blue complex number is the difference between C₁ and C₂ .

5.1 Extract real and imaginary numbers from complex numbers

IMSUB function chart the difference5

Make sure that each complex number begins with real value 0 and imaginary value 0 on a separate row except the complex number you subtract with (green). The real and imaginary values on the next row, and that there is an empty row between. You can use the IMREAL function and the IMAGINARY function to extract the coordinates from the complex numbers in column B, make sure they are in rectangular form.

Formula in cell C25:

=IMREAL(B25)

Formula in cell D25:

=IMREAL(B25)

Copy these cells and paste to cells C28 and D28 respectively.

Formula in cell B31:

=IMSUB(B25, B28)

The row before complex number 2-4i (row 27) must contain the result from cells C31 and D31.

5.2 Insert scatter chart

IMSUB function chart the difference6

Select cell range C24:D31.
Go to tab "Insert" on the ribbon.
Press with mouse on the icon named "Insert Scatter (x,y)", a popup menu appears.
Press with left mouse button on the icon "Scatter with Straight Lines and Markers".
The chart shows up on the worksheet.

Press and hold with left mouse button on the chart border, then drag it to the location you want. Use the "handles" to resize the chart, see the image below.

IMSUB function chart the difference8

5.3 Create arrows and change colors

IMSUB function chart the difference9

Double-press with left mouse button on with left mouse button on one of the lines on the chart, all lines will be selected and a settings pane shows up.
Press with left mouse button on the "Fill&Line" button.
Press with mouse on "End Arrow type", select an arrow.
Press with mouse on "End Arrow size, pick a size.

IMSUB function chart the difference12

Press with left mouse button on twice on a line to select a specific line.
Press with left mouse button on the color button on the settings pane. A popup menu appears.
Pick a color.
Repeat steps 1 to 3 with remaining lines.

IMSUB function chart the difference14

There are still three markers on the chart, here is how to remove them.

Select all the lines by press with left mouse button oning on them once.
Go to the settings pane.
Press with left mouse button on "Marker Options".
Select "None".

IMSUB function chart the difference16

5.4 Change axis min and max value

IMSUB function chart the difference17

Double-press with left mouse button on one of the y-axis to open the settings pane.
Press with left mouse button on the "Axis Options" button.
Change the Bounds and the Units.
Repeat step 1 to 3 with the x-axis.

IMSUB function chart the difference19

5.5 Change axis markers and line width

Select the y-axis.
Press with left mouse button on the "Fill & Line" button.
Press with left mouse button on the "Line".
Press with left mouse button on the "Color" button. Press with mouse on black.
Change the width to 1.5

IMSUB function chart the difference21

Press with right mouse button on on one of the lines, a popup menu appears.
Press with mouse on "Add Data Labels".
Double-press with left mouse button on one of the data labels, the settings pane shows up.
Select "X Value" as well.

IMSUB function chart the difference24

Change the chart title and add axis titles.

6. How to calculate the distance between two complex numbers?

How to calculate the distance between two complex numbers1

The following formula calculates the length between two complex numbers in the complex plane. First, the formula subtracts the second complex number from the first, then it calculates the modulus of the difference.

For example, the first complex number is -2+2i and the second complex number is 4+4i. The difference is -6-2i, the modulus of -6-2i is the square root of 40 which equals approx. 6.32

Formula in cell E2:

=IMABS(IMSUB(C2,C3))

The image above shows the distance between these two points on the complex plane, the distance is the dashed blue line between -2+2i and 4+4i.

Explaining formula in cell E2

Step 1 - Calculate the difference between two complex numbers

The IMSUB function calculates the difference between two complex numbers in x + yi or x + yj text format.

Function syntax: IMSUB(inumber1, inumber2)

IMSUB(C2,C3)

becomes

IMSUB("-2+2i","4+4i")

and returns

"-6-2i"

Step 2 - Calculate the modulus of a complex number

The IMABS function calculates the absolute value (modulus) of a complex number in x + yi or x + yj text format.

Function syntax: IMABS(inumber)

IMABS(IMSUB(C2,C3))

becomes

IMABS("-6-2i")

and returns

6.32

Functions in 'Engineering' category

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

BIN2DEC function

Converts a binary number to the decimal number system.

BIN2HEX function

Converts a binary number to hexadecimal.

BIN2OCT function

Converts a binary number to octal.

BITAND function

Calculates a bitwise 'AND' of two numbers.

BITLSHIFT function

Calculates a number whose binary representation is shifted left by a specified number of bits.

BITOR function

Performs a bitwise 'OR' of two numbers.

BITRSHIFT function

Calculates the number where the binary equivalent is shifted right by a specified number of bits and then converted back to a number.

BITXOR function

Calculates a decimal number that is a result of a bitwise comparison "XOR" of two numbers.

COMPLEX function

Returns a complex number based on a real and imaginary number.

CONVERT function

Converts a number from one measurement system to another.

DEC2BIN function

Converts a decimal number to a binary number.

DEC2HEX function

Converts a decimal number to a hexadecimal number.

DEC2OCT function

Converts a decimal number to an octal number.

DELTA function

Evaluates whether two numerical values are equal.

HEX2BIN function

Converts a hexadecimal number to a binary number.

HEX2DEC function

Converts a hexadecimal number to a decimal number.

HEX2OCT function

Converts hexadecimal to octal.

IMABS function

Calculates the absolute value (modulus) of a complex number in x + yi or x + yj text format.

IMAGINARY function

Calculates the imaginary value of a complex number in x + yi or x + yj text format.

IMARGUMENT function

Calculates theta θ which is an angle displayed in radians based on complex numbers in rectangular form.

IMCONJUGATE function

Calculates the complex conjugate of a complex number in x + yi or x + yj text format.

IMCOS function

Calculates the cosine of a complex number in x + yi or x + yj text format.

IMCOSH function

Calculates the hyperbole cosine of a complex number in x + yi or x + yj text format.

IMCOT function

Calculates the cotangent of a complex number in x + yi or x + yj text format.

IMCSC function

Calculates the cosecant of a complex number in x + yi or x + yj text format.

IMCSCH function

Calculates the hyperbolic cosecant of a complex number in x + yi or x + yj text format.

IMDIV function

Calculates the quotient of two complex numbers in x + yi or x + yj text format.

IMEXP function

Calculates the exponential of a complex number in x + yi or x + yj text format.

IMLN function

Calculates the natural logarithm of a complex number in x + yi or x + yj text format.

IMLOG10 function

Calculates the base 10 logarithm of a complex number in x + yi or x + yj text format.

IMLOG2 function

Calculates the base 2 logarithm of a complex number in x + yi or x + yj text format.

IMPOWER function

Calculates a complex number raised to a given power in x + yi or x + yj text format.

IMPRODUCT function

Calculates the product of complex numbers in x + yi or x + yj text format.

IMREAL function

Calculates the real coefficient of a complex number in x + yi or x + yj text format.

IMSEC function

Calculates the secant of a complex number in x + yi or x + yj text format.

IMSECH function

Calculates the hyperbolic secant of a complex number in x + yi or x + yj text format.

IMSIN function

Calculates the sine of a complex number in x + yi or x + yj text format.

IMSINH function

Calculates the hyperbolic sine of a complex number in x + yi or x + yj text format.

IMSQRT function

Calculates the square root of a complex number in x + yi or x + yj text format.

IMSUB function

Calculates the difference between two complex numbers in x + yi or x + yj text format.

IMSUM function

Calculates the total of two or more complex numbers in x + yi or x + yj text format.

IMTAN function

Calculates the tangent of a complex number in x + yi or x + yj text format.

Excel function categories

Array manipulation

Excel functions that let you resize, combine, and shape arrays.

Compatibility

Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.

Database

Perform basic operations to a database-like structure.

Date and Time

Functions that let you perform calculations to Excel date and time values.

Engineering

Let's you manipulate binary numbers, convert values between different numeral systems, and calculate imaginary numbers.

Financial

Calculate present value, interest, accumulated interest, principal, accumulated principal, depreciation, payment, price, growth, yield for securities, and other financial calculations.

Information

Functions that let you get information from a cell, formatting, formula, worksheet, workbook, filepath, and other entitites.

Logical

Functions that let you return and manipulate logical values, and also control formula calculations based on logical expressions.

Lookup and reference

These functions let you sort, lookup, get external data like stock quotes, filter values based a condition or criteria, and get the relative position of a given value in a specific cell range. They also let you calculate row, column, and other properties of cell references.

Math and trigonometry

You will find functions in this category that calculates random values, round numerical values, create sequential numbers, trigonometry, and more.

Statistical

Calculate distributions, binomial distributions, exponential distribution, probabilities, variance, covariance, confidence interval, frequency, geometric mean, standard deviation, average, median, and other statistical metrics.

Text

Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.

Web

Get data from the internet, extract data from an XML string and more.

Excel categories

Home page

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Excel Functions

More than 300 Excel functions with detailed information including syntax, arguments, return values, and examples for most of the functions used in Excel formulas.

Excel Formulas

More than 1300 formulas organized in subcategories.

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Excel Tables simplifies your work with data, adding or removing data, filtering, totals, sorting, enhance readability using cell formatting, cell references, formulas, and more.

Advanced Filter

Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.

Data Validation

Lets you control what a user can type into a cell. It allows you to specifiy conditions and show a custom message if entered data is not valid.

Drop Down List

Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.

Named Ranges

Lets you name one or more cells, this makes it easier to find cells using the Name box, read and understand formulas containing names instead of cell references.

Excel Solver

The Excel Solver is a free add-in that uses objective cells, constraints based on formulas on a worksheet to perform what-if analysis and other decision problems like permutations and combinations.

Charts

An Excel feature that lets you visualize data in a graph.

Conditonal Formatting

Format cells or cell values based a condition or criteria, there a multiple built-in Conditional Formatting tools you can use or use a custom-made conditional formatting formula.

Pivot Tables

Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.

VBA

VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.

Macros

A program or subroutine built in VBA that anyone can create. Use the macro-recorder to quickly create your own VBA macros.

UDFs

UDF stands for User Defined Functions and is custom built functions anyone can create.

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