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In this comprehensive guide, we will explore the IMSUM function in Excel, which is used to add complex numbers. Complex numbers are numbers that consist of a real part and an imaginary part, represented as “a + bi” where “a” is the real part, “b” is the imaginary part, and “i” is the imaginary unit. The IMSUM function is particularly useful for engineers, mathematicians, and scientists who work with complex numbers in their calculations.

IMSUM Syntax

The syntax for the IMSUM function is as follows:

=IMSUM(number1, [number2], …)


  • number1 is the first complex number you want to add. This argument is required.
  • number2, … are additional complex numbers you want to add. These arguments are optional, and you can add up to 29 additional complex numbers.

Each complex number should be entered as a text string, enclosed in double quotes. The real and imaginary parts should be separated by a plus or minus sign, followed by the imaginary part with an “i” or “j” suffix. For example, “3+4i” or “5-2j”.

IMSUM Examples

Here are some examples of how to use the IMSUM function in Excel:

  1. Adding two complex numbers: To add the complex numbers 3 + 4i and 5 – 2i, you would use the formula =IMSUM(“3+4i”, “5-2i”). The result would be “8+2i”.
  2. Adding multiple complex numbers: To add the complex numbers 1 + 2i, 3 + 4i, and 5 + 6i, you would use the formula =IMSUM(“1+2i”, “3+4i”, “5+6i”). The result would be “9+12i”.
  3. Adding complex numbers with different imaginary unit notations: To add the complex numbers 2 + 3i and 4 – 5j, you would use the formula =IMSUM(“2+3i”, “4-5j”). The result would be “6-2i”. Note that Excel automatically converts the “j” notation to “i” in the result.

IMSUM Tips & Tricks

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

  • Remember to enclose complex numbers in double quotes and separate the real and imaginary parts with a plus or minus sign, followed by the imaginary part with an “i” or “j” suffix.
  • If you have a list of complex numbers in a range of cells, you can use the IMSUM function with an array formula to add them all together. For example, if you have complex numbers in cells A1:A5, you can use the formula =IMSUM(A1:A5) and press Ctrl+Shift+Enter to enter it as an array formula.
  • You can also use the IMSUM function in combination with other complex number functions in Excel, such as IMABS, IMARGUMENT, IMCONJUGATE, and IMREAL, to perform more advanced calculations with complex numbers.

Common Mistakes When Using IMSUM

Here are some common mistakes to avoid when using the IMSUM function:

  • Not enclosing complex numbers in double quotes. Make sure to enter complex numbers as text strings, enclosed in double quotes.
  • Using incorrect notation for the imaginary part. Remember to use “i” or “j” as the suffix for the imaginary part, and separate it from the real part with a plus or minus sign.
  • Forgetting to press Ctrl+Shift+Enter when using IMSUM with an array formula. If you’re adding a range of complex numbers, make sure to enter the formula as an array formula by pressing Ctrl+Shift+Enter.

Why Isn’t My IMSUM Working?

If your IMSUM function isn’t working as expected, here are some possible reasons and solutions:

  • Error in complex number notation: Double-check that you’ve entered the complex numbers correctly, with the real and imaginary parts separated by a plus or minus sign, and the imaginary part followed by an “i” or “j” suffix.
  • Missing double quotes: Ensure that each complex number is enclosed in double quotes, as IMSUM requires complex numbers to be entered as text strings.
  • Incorrect use of array formula: If you’re using IMSUM with an array formula, make sure to press Ctrl+Shift+Enter to enter the formula correctly.
  • Invalid arguments: Check that you haven’t entered any invalid arguments, such as non-complex numbers or text that doesn’t represent a complex number.

IMSUM: Related Formulae

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

  1. IMPRODUCT: This function multiplies complex numbers. Syntax: =IMPRODUCT(number1, [number2], …)
  2. IMDIV: This function divides one complex number by another. Syntax: =IMDIV(inumber1, inumber2)
  3. IMSUB: This function subtracts one complex number from another. Syntax: =IMSUB(inumber1, inumber2)
  4. IMCONJUGATE: This function returns the complex conjugate of a complex number. Syntax: =IMCONJUGATE(inumber)
  5. IMABS: This function returns the absolute value (modulus) of a complex number. Syntax: =IMABS(inumber)

By mastering the IMSUM function and related formulae, you’ll be well-equipped to perform calculations with complex numbers in Excel. Whether you’re an engineer, mathematician, or scientist, these functions can help you streamline your work and improve your efficiency.


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