In this comprehensive guide, we will explore the IMAGINARY function in Excel, which is used to extract the imaginary part of a complex number. Complex numbers are numbers that consist of a real part and an imaginary part, and they are represented in the form of a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (i� = -1). The IMAGINARY function is particularly useful when working with complex numbers in various mathematical and engineering calculations.


The syntax for the IMAGINARY function in Excel is quite simple:



  • complex_number (required) – This is the complex number from which you want to extract the imaginary part. It can be entered as a text string (e.g., “3+4i”) or as a reference to a cell containing a complex number.


Let’s look at some examples of how to use the IMAGINARY function in Excel:

Example 1: Basic usage of the IMAGINARY function


This formula will return the value 4, which is the imaginary part of the complex number 3+4i.

Example 2: Using a cell reference as the complex_number argument


Assuming cell A1 contains the complex number “5-2i”, this formula will return the value -2, which is the imaginary part of the complex number 5-2i.

Example 3: Combining the IMAGINARY function with other functions


This formula first calculates the complex conjugate of the complex number 3+4i, which is 3-4i, and then extracts the imaginary part, returning the value -4.

IMAGINARY Tips & Tricks

Here are some tips and tricks to help you get the most out of the IMAGINARY function in Excel:

  1. Remember that the IMAGINARY function only returns the imaginary part of a complex number. If you need to extract the real part, use the REAL function.
  2. If you need to perform calculations with complex numbers, consider using other Excel functions designed for complex numbers, such as COMPLEX, IMABS, IMARGUMENT, IMCONJUGATE, IMDIV, IMEXP, IMLN, IMLOG10, IMLOG2, IMPOWER, IMPRODUCT, IMREAL, IMSIN, IMSQRT, IMSUB, IMSUM, and IMTAN.
  3. When entering complex numbers as text strings, make sure to use the correct format (a + bi or a – bi), and avoid using spaces between the real and imaginary parts.

Common Mistakes When Using IMAGINARY

Here are some common mistakes that users make when using the IMAGINARY function in Excel:

  1. Forgetting to include the “i” in the complex number. The IMAGINARY function will return an error if the complex number is not formatted correctly.
  2. Using spaces between the real and imaginary parts of the complex number. This can cause the IMAGINARY function to return an error.
  3. Not using quotation marks when entering a complex number as a text string. If you don’t use quotation marks, Excel will treat the complex number as a formula, which will result in an error.

Why Isn’t My IMAGINARY Function Working?

If you’re having trouble with the IMAGINARY function, consider the following troubleshooting steps:

  1. Double-check the format of your complex number. Make sure it is in the form of a + bi or a – bi, with no spaces between the real and imaginary parts.
  2. Ensure that you’re using the correct syntax for the IMAGINARY function, including the correct number of arguments and the correct argument types.
  3. Check for any errors in your formula, such as missing or extra parentheses, incorrect cell references, or misspelled function names.

IMAGINARY: Related Formulae

Here are some related formulae that you might find useful when working with complex numbers in Excel:

  1. COMPLEX: This function creates a complex number from a given real part and imaginary part. Syntax: =COMPLEX(real_part, imaginary_part)
  2. IMREAL: This function returns the real part of a complex number. Syntax: =IMREAL(complex_number)
  3. IMABS: This function returns the absolute value (modulus) of a complex number. Syntax: =IMABS(complex_number)
  4. IMCONJUGATE: This function returns the complex conjugate of a complex number. Syntax: =IMCONJUGATE(complex_number)
  5. IMSUM: This function returns the sum of two or more complex numbers. Syntax: =IMSUM(complex_number1, complex_number2, …)

By mastering the IMAGINARY function and related formulae, you’ll be well-equipped to handle complex numbers in your Excel calculations, whether you’re working on mathematical problems, engineering tasks, or any other application that requires the manipulation of complex numbers.


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