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Real and Imaginary Part Calculator

Reviewed by Calculator Editorial Team

A complex number is a combination of a real number and an imaginary number. This calculator helps you separate these components from any given complex number.

What is a complex number?

Complex numbers extend the concept of ordinary numbers to include solutions to equations that don't have real solutions. They are written in the form:

z = a + bi

where:

  • z is the complex number
  • a is the real part
  • b is the imaginary part
  • i is the imaginary unit (√-1)

The real part (a) is the ordinary number component, while the imaginary part (b) is multiplied by the imaginary unit i. Complex numbers are fundamental in advanced mathematics, engineering, and physics.

How to extract real and imaginary parts

To separate the real and imaginary components of a complex number:

  1. Identify the real number coefficient (a)
  2. Identify the coefficient of the imaginary unit (b)
  3. Express the complex number in standard form a + bi

For example, in the complex number 3 + 4i:

  • Real part = 3
  • Imaginary part = 4

This calculator automates this process for any valid complex number input.

Using the calculator

Enter a complex number in the format a + bi or a - bi, then click Calculate. The calculator will display the real and imaginary parts separately.

Examples of valid inputs:

  • 3 + 4i
  • -2 - 5i
  • 7.5 + 2.3i

Worked examples

Example 1: Simple complex number

For the complex number 5 + 2i:

  • Real part = 5
  • Imaginary part = 2

Example 2: Negative components

For the complex number -3 - 4i:

  • Real part = -3
  • Imaginary part = -4

Example 3: Decimal components

For the complex number 1.5 + 0.75i:

  • Real part = 1.5
  • Imaginary part = 0.75

FAQ

What is the difference between real and imaginary parts?
The real part is the ordinary number component, while the imaginary part is multiplied by the imaginary unit i (√-1).
Can I use this calculator for polar form complex numbers?
This calculator works with standard rectangular form (a + bi). For polar form, you would need a different conversion tool.
What if my complex number has no imaginary part?
The calculator will identify the entire number as the real part with an imaginary part of 0.