1. What Are Imaginary Numbers?

Imaginary numbers are numbers that when squared give a negative result. The imaginary unit is denoted by i, where i² = -1. Complex numbers combine real and imaginary numbers in the form a + bi.

2. How Does the Calculator Work?

The calculator uses the standard complex number formula:

Where:

• \( a \) — Real part of the complex number
• \( b \) — Imaginary part of the complex number
• \( i \) — Imaginary unit (√-1)

Explanation: The calculator combines the real and imaginary components to form a standard complex number representation.

3. Importance of Complex Numbers

Details: Complex numbers are fundamental in many areas of mathematics, physics, and engineering, particularly in electrical engineering, quantum mechanics, and signal processing.

4. Using the Calculator

Tips: Enter the real and imaginary components of your complex number. The calculator will format it in standard a + bi form.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between real and imaginary numbers?
A: Real numbers can be plotted on a number line, while imaginary numbers involve the square root of negative numbers.

Q2: What are complex numbers used for?
A: They're used in AC circuit analysis, quantum physics, fluid dynamics, and many other scientific fields.

Q3: How do you add two complex numbers?
A: Add the real parts and the imaginary parts separately: (a+bi) + (c+di) = (a+c) + (b+d)i

Q4: What is the complex conjugate?
A: For a complex number a+bi, its conjugate is a-bi.

Q5: How do you multiply complex numbers?
A: Use the distributive property and remember that i² = -1: (a+bi)(c+di) = (ac-bd) + (ad+bc)i