1. What is an Imaginary Number?

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, where i² = -1. A complex number has both real and imaginary parts (a + bi).

2. How Does the Calculator Work?

The calculator extracts the real part from an imaginary or complex number:

Where:

• \( \Re(z) \) — Real part of complex number z
• Pure imaginary — Number in the form bi (e.g., 3i)
• Complex — Number in the form a + bi (e.g., 4+5i)

Explanation: For pure imaginary numbers, the real part is always 0. For complex numbers, the real part is the coefficient not multiplied by i.

3. Importance of Real Part Extraction

Details: Extracting the real part is essential in signal processing, electrical engineering, and physics where complex numbers represent waveforms and alternating currents.

4. Using the Calculator

Tips: Enter the imaginary number in the form "3i" for pure imaginary or "4+5i" for complex numbers. The calculator will return the real part (0 for pure imaginary).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between imaginary and complex numbers?
A: Pure imaginary numbers have no real part (bi), while complex numbers have both real and imaginary parts (a + bi).

Q2: Why is the real part 0 for pure imaginary numbers?
A: By definition, pure imaginary numbers have no real component - they exist entirely on the imaginary axis.

Q3: How are complex numbers used in real-world applications?
A: They're fundamental in electrical engineering (AC circuits), quantum mechanics, signal processing, and fluid dynamics.

Q4: What if I enter just a real number?
A: The calculator will return the number itself, as real numbers are their own real part with 0 imaginary component.

Q5: Can this calculator handle complex expressions?
A: This version handles basic forms (bi or a+bi). For advanced expressions, a full complex number calculator would be needed.