IMSUM function

The IMSUM function in Excel adds two or more complex numbers.

Syntax

IMSUM(inumber1, inumber2, ...)

Parameters

• inumber1, inumber2, ...: The complex numbers you want to add. You can provide up to 255 complex numbers as arguments. Each complex number can be input as a text string (e.g., "a + bi" or "a + bj"), where a is the real part and b is the imaginary part. You can also use cell references containing complex numbers.

How It Works

The IMSUM function adds two or more complex numbers. If $z_1 = a + bi$ and $z_2 = c + di$, the result is given by:

$$z_1 + z_2 = (a + c) + (b + d)i$$

Where:

• a and b are the real and imaginary parts of the first complex number,
• c and d are the real and imaginary parts of the second complex number.

If you add more than two complex numbers, the function will perform the addition step by step for all provided complex numbers.

Examples

1. Adding Two Complex Numbers: To add the complex numbers 2 + 3i and 4 + 5i:

   =IMSUM("2+3i", "4+5i")
   

   The result will be 6 + 8i, which is the sum of the two complex numbers.

2. Using Cell References: If cell A1 contains "1+2i" and cell A2 contains "3+4i", you can calculate the sum using:

   =IMSUM(A1, A2)
   

   The result will be 4 + 6i, which is the sum of the complex numbers in cells A1 and A2.

3. Adding More Than Two Complex Numbers: If you want to add three complex numbers, "1+2i", "3+4i", and "5+6i", you can use:

   =IMSUM("1+2i", "3+4i", "5+6i")
   

   The result will be 9 + 12i, which is the sum of the three complex numbers.

Important Notes

• The IMSUM function only works with valid complex numbers. If any of the inputs is not a valid complex number, Excel will return a #VALUE! error.
• Complex numbers can be written using either i or j for the imaginary part.
• The result will also be a complex number, as the sum of complex numbers is another complex number.

Summary

The IMSUM function in Excel is used to add two or more complex numbers. It is valuable for mathematical, engineering, or scientific applications where you need to add complex numbers.