Complex Number Calculator
This calculator is designed for students, engineers, and professionals dealing with complex numbers. It allows you to perform arithmetic operations on complex numbers quickly and accurately.
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Data Source and Methodology
All calculations are based on standard mathematical principles for complex numbers. For more detailed explanations, refer to Symbolab. All calculations strictly adhere to the data and formulas provided by this source.
The Formula Explained
The magnitude of a complex number \( z = a + bi \) is calculated using the formula: \( \sqrt{a^2 + b^2} \). The angle (in radians) is calculated as \( \arctan(\frac{b}{a}) \).
Glossary of Terms
- Real Part: The real component of the complex number.
- Imaginary Part: The imaginary component of the complex number.
- Magnitude: The distance of the complex number from the origin in the complex plane.
- Angle (Radians): The angle formed with the positive real axis in the complex plane.
How It Works: A Step-by-Step Example
Consider the complex number \( z = 3 + 4i \). To find the magnitude, compute \( \sqrt{3^2 + 4^2} = 5 \). The angle is \( \arctan(\frac{4}{3}) \).
Frequently Asked Questions (FAQ)
What is a complex number?
A complex number is a number that comprises a real part and an imaginary part.
How do you add complex numbers?
To add complex numbers, add their real parts and their imaginary parts separately.
How do you multiply complex numbers?
Use the distributive property and the fact that \( i^2 = -1 \) to multiply complex numbers.
What is the conjugate of a complex number?
The conjugate of a complex number \( z = a + bi \) is \( a - bi \).
How do you divide complex numbers?
Multiply the numerator and the denominator by the conjugate of the denominator and simplify.