Excel IMSUM and IMPRODUCT Functions
last modified April 4, 2025
The IMSUM and IMPRODUCT functions are specialized
Excel functions for working with complex numbers. They perform addition and
multiplication operations on complex numbers in the form x+yi or x+yj.
This tutorial provides a comprehensive guide to using these functions with
detailed examples. You'll learn basic syntax, practical applications, and
advanced techniques.
IMSUM/IMPRODUCT Function Basics
The IMSUM function adds complex numbers, while IMPRODUCT
multiplies them. Both functions handle complex numbers in text format.
| Function | Description | Syntax |
|---|---|---|
| IMSUM | Returns the sum of complex numbers | =IMSUM(inumber1, [inumber2], ...) |
| IMPRODUCT | Returns the product of complex numbers | =IMPRODUCT(inumber1, [inumber2], ...) |
This table shows the essential components of both functions. They accept 1-255 complex numbers as arguments and return a complex number as text.
Basic IMSUM Example
This example demonstrates the simplest use of the IMSUM function with two complex numbers.
=IMSUM("3+4i", "1+2i")
This formula adds two complex numbers: 3+4i and 1+2i. The result will be "4+6i". The function adds the real parts (3+1) and imaginary parts (4+2) separately.
Basic IMPRODUCT Example
This example shows the basic multiplication of two complex numbers using IMPRODUCT.
=IMPRODUCT("2+3i", "1+4i")
This formula multiplies 2+3i by 1+4i. The result is "-10+11i" because: (2*1 - 3*4) + (2*4 + 3*1)i = (2-12) + (8+3)i = -10 + 11i.
IMSUM with Cell References
A more practical use involves adding complex numbers stored in cells. Here's an example with cell references.
| A | B |
|---|---|
| 5+2i | |
| 3+7i | |
| =IMSUM(A1, A2) |
The table shows complex numbers in column A and an IMSUM formula in cell B3 that adds them. The result will be "8+9i" (5+3 real parts, 2+7 imaginary).
=IMSUM(A1, A2)
This formula sums complex numbers in cells A1 and A2. Using cell references makes the function more flexible for working with spreadsheet data.
IMPRODUCT with Multiple Numbers
IMPRODUCT can multiply several complex numbers at once. This example shows multiplication of three complex numbers.
=IMPRODUCT("1+i", "2+3i", "1-i")
This formula multiplies three complex numbers step by step. First 1+i and 2+3i give -1+5i, then multiplied by 1-i gives 4+6i. The final result is "4+6i".
IMSUM with Real Numbers
IMSUM can handle regular numbers by treating them as complex numbers with zero imaginary part. This example demonstrates this behavior.
=IMSUM("5", "3+2i")
The formula adds 5 (treated as 5+0i) and 3+2i. The result is "8+2i". This shows how IMSUM seamlessly handles mixing real and complex numbers.
IMPRODUCT with Polar Form
Excel can convert between rectangular and polar forms. This example shows IMPRODUCT with complex numbers in polar form.
=IMPRODUCT(COMPLEX(3,4), COMPLEX(1,2))
This formula uses the COMPLEX function to create numbers from components, then multiplies them. The result is identical to direct text input: "-5+10i" for these values.
IMSUM with Array of Numbers
IMSUM can work with arrays of complex numbers. This example demonstrates summing multiple complex values.
=IMSUM({"1+2i","3+4i","5+6i"})
This formula sums three complex numbers in an array. The result is "9+12i" (1+3+5 real parts, 2+4+6 imaginary). Array input makes bulk operations convenient.
Error Handling
Both functions return errors for invalid complex number formats. This example shows error handling.
=IMSUM("3+4i", "invalid")
This formula returns #NUM! error because the second argument isn't a valid complex number. Proper formatting like "x+yi" or "x+yj" is required for both functions to work correctly.
The IMSUM and IMPRODUCT functions are essential for
engineering and scientific calculations involving complex numbers. They handle
both rectangular and polar forms, and work seamlessly with real numbers.
Mastering these functions expands Excel's capabilities for advanced
mathematical operations.
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