IMSUB function

The IMSUB function in Excel subtracts one complex number from another.

Syntax

IMSUB(inumber1, inumber2)

Parameters

• inumber1: The first complex number (minuend) from which the second complex number will be subtracted. It can be input as a text string like a + bi or a + bj, where a is the real part and b is the imaginary part.
• inumber2: The second complex number (subtrahend) to subtract from the first. It can also be input as a text string in the same format as the first complex number.

How It Works

The IMSUB function subtracts one complex number from another. 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.

Examples

1. Subtracting Two Complex Numbers: To subtract the complex number 3 + 4i from 5 + 6i:

   =IMSUB("5+6i", "3+4i")
   

   The result will be 2 + 2i, which is the difference between the two complex numbers.

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

   =IMSUB(A1, A2)
   

   The result will be 3 + 1i, which is the difference between the complex numbers in cells A1 and A2.

3. Subtracting a Complex Number from a Purely Imaginary Number: If you subtract "3+4i" from "0+2i":

   =IMSUB("0+2i", "3+4i")
   

   The result will be -3 - 2i, which represents the difference between the two complex numbers.

Important Notes

• The IMSUB 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 subtraction of two complex numbers results in another complex number.

Summary

The IMSUB function in Excel is used to subtract one complex number from another. It is useful for advanced mathematical, engineering, or scientific calculations involving complex numbers.