How to use the IMAGINARY() function in Excel

Its extracts the imaginary coefficient (y) from a complex number in the form x + yi or x + yj.

Syntax
IMAGINARY(complex_number)

Argument

• complex_number (required)
  A text string representing a complex number in either:
  • « x+yi » format (mathematical convention)
  • « x+yj » format (engineering convention)
  • Examples: « 3-4i », « 5+2j », « -1+7i »

Technical Background
For a complex number z = a + bi:

• a is the real part (extracted with IMREAL())
• b is the imaginary part (extracted with IMAGINARY())
• i (or j) is the imaginary unit (√-1)

Example

=IMAGINARY(« 3-4i »)  // Returns -4

Key Features

• Supports both « i » and « j » notation
• Returns a real number value
• Handles positive/negative coefficients
• Returns 0 for pure real numbers

Error Conditions

• Returns #NUM! for:
  • Invalid complex number format
  • Missing imaginary unit when imaginary part exists
  • Non-numeric components

Usage Notes

1. Input must be text string in proper complex format
2. The sign of the imaginary part is preserved
3. For engineering applications, use « j » notation
4. Combine with IMREAL() to separate complex components