This guide will explain how to use the IMPRODUCT function in Google Sheets.
When we need to multiply a series of complex numbers together, we can easily do this using the IMPRODUCT function in Google Sheets.
The rules for using the IMPRODUCT function in Google Sheets are the following:
- The
IMPRODUCTfunction supports both real and complex numbers. - If we input a complex number, it must be in the a+bi format.
- We can input up to 30 additional values or ranges in the
IMPRODUCTformula. - The complex number must be entered as a text string.
- We can only multiply complex numbers if they have the same suffix. For example, all given complex numbers must use the suffix i.
Google Sheets has a wide range of built-in functions dedicated to simplifying working with complex numbers, making it easier to use in different situations.
Complex numbers consist of a real and imaginary part, represented as a +bi, where a and b are real numbers, and i is an imaginary unit. Hence, the IMPRODUCT function is utilized to multiply a series of complex numbers together.
In this guide, we will provide a step-by-step tutorial on how to use the IMPRODUCT function in Google Sheets. Additionally, we will explore the syntax and a real example of using the function.
Great! Let’s dive right in.
The Anatomy of the IMPRODUCT Function
The syntax or the way we write the IMPRODUCT function is as follows:
=IMPRODUCT(factor1,[factor2,...])
- = the equal sign is how we begin any function in Google Sheets.
- IMPRODUCT() is our
IMPRODUCTfunction. This function will return the result of multiplying a series of complex numbers together. - factor1 is the only required argument. This refers to the first complex number or range to calculate for the product.
- factor2 is an optional argument. This refers to additional values or ranges we want to multiply. We can input up to 30 additional values or ranges.
Note: The IMPRODUCT function can support both real and complex numbers.
The Anatomy of the ARRAYFORMULA Function
The syntax or the way we write the ARRAYFORMULA function is as follows:
=ARRAYFORMULA(array_formula)
- = the equal sign is how we activate any function in Google Sheets.
- ARRAYFORMULA() refers to our
ARRAYFORMULAfunction. This function enables the display of values returned from an array formula into multiple rows and/or columns and the use of non-array functions with arrays. - array_formula is the only required argument. This refers to a range, a mathematical expression using one cell or multiple ranges of the same size, or a function that returns a result greater than one cell.
Note: You can also press Ctrl+Shift+Enter while editing a formula to automatically add ARRAYFORMULA( to the beginning of the formula.
Common Mistakes in Using IMPRODUCT Function
The IMPRODUCT function has a straightforward syntax making it simple to use. However, we still need to be careful when using some things to ensure the function properly works.
Firstly, ensure to enter the complex numbers as text strings. The complex numbers must be in the format “a+bi” or “a-bi”. Otherwise, Google Sheets may not recognize them as complex numbers, and the formula may not work as expected.
Secondly, the given numbers must have the same suffix. We can only multiply complex numbers having the same suffix, such as i or j. For instance, we cannot multiply (4+5i, 2+4j) using the IMPRODUCT function.
Thirdly, make sure we have not exceeded the limit of 30 additional values or ranges in the formula. If we need to multiply more than 30 values, we can use multiple IMPRODUCT formulas and then multiply the results together.
Lastly, check the syntax of the formula. Ensure the syntax of the function call is correct, including the proper placement of commas, the use of parentheses, and the quotation marks for the complex number.
A Real Example of Using IMPRODUCT Function in Google Sheets
Let’s say we have two complex numbers we want to multiply together. Our initial data set would look like this:
The product of two complex numbers is defined as follows: (a+bi)(c+di) = (ac-bd) + (ad+bc)i.
We will use the formula below:
=IMPRODUCT(A2,A3)
The formula only has one argument, which refers to the complex numbers we want to multiply. In this case, we simply selected cells A2 and A3, which contain complex numbers.
Our final data set would look like this:
Let’s say we have a data set containing a list of complex numbers we want to multiply. Our initial data set would look like this:
We can insert the ARRAYFORMULA function at the beginning of our formula to easily multiply the series of complex numbers without entering a long list of individual cell references in the formula.
Our formula would become:
=ARRAYFORMULA(IMPRODUCT(A7:A13))
In this formula, we selected the range A7:A13 containing the complex numbers. The ARRAYFORMULA function will apply the IMPRODUCT function to each cell in the range. Then, the formula will return the result of multiplying a series of complex numbers together.
Our final data set using the ARRAYFORMULA would look like this:
You can make your own copy of the spreadsheet above using the link below.
Amazing! Now we can dive into the steps of using the IMPRODUCT function in Google Sheets.
How to Use IMPRODUCT Function in Google Sheets
1. First, we will select an empty cell to input the formula and display the result of multiplying a series of complex numbers.
2. To start, we will type in an equal sign and the function name. Our formula would be “=IMPRODUCT(”.
3. We will simply select the cell containing the first complex number we want to multiply. Our final formula would be “=IMPRODUCT(A2”.
4. Then, we will simply select the cell containing the other complex number we want to multiply. Our final formula would be “=IMPRODUCT(A2,A3)”.
5. We will press the Enter key to return the result.
6. Let’s say we have a list of complex numbers to multiply. In this case, we will combine the ARRAYFORMULA with our IMPRODUCT formula. We will start with an equal sign and the ARRAYFORMULA function. Our formula would become “=ARRAYFORMULA(”.
7. Then, we will type in the IMPRODUCT function. In this case, our formula would become “=ARRAYFORMULA(IMPRODUCT(”.
8. Next, we will select the entire range containing the complex numbers. Our final formula would become “=ARRAYFORMULA(IMPRODUCT(A7:A13))”.
9. We will press the Enter key to return the result.
And tada! We have successfully used the IMPRODUCT function in Google Sheets.
You can apply this guide whenever you need to multiply a series of complex numbers together. You can now use the IMPRODUCT function and the various other Google Sheets formulas available to create great worksheets that work for you.
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