How to use the IMSUB() function in Excel

This function returns the difference between two complex numbers, which must be strings in the format x + yi or x + yj.

Syntax
IMSUB(complex_number1; complex_number2)

Arguments

• complex_number1 (required)
  The complex minuend (number to be subtracted from)
• complex_number2 (required)
  The complex subtrahend (number to subtract)

Background
The difference between two complex numbers is calculated by separately subtracting their real and imaginary components:

(a + bi) – (c + di) = (a – c) + i·(b – d)

The basics of complex numbers are described in the section titled Functions for Complex Numbers.

Example
The following example illustrates this function:

=IMSUB(« 3-4i », »-7-24i ») returns 10+20i

Key Features

• Handles both « i » and « j » notation
• Maintains component-wise precision
• Preserves the imaginary unit from the first argument
• Returns result in standard rectangular form

Technical Notes

1. Real and imaginary parts are subtracted independently
2. For complex conjugates:
   (a+bi) – (a-bi) = 0+2bi
3. Essential for:
   • Complex vector calculations
   • Circuit analysis
   • Signal processing

Error Conditions

• Returns #NUM! for:
  • Invalid complex number format
  • Non-numeric components
  • Mismatched imaginary units