Complex Number Calculator
Free online complex number calculator. Perform addition, subtraction, multiplication, and division of complex numbers (a + bi). View results in rectangular and polar forms.
About Complex Number Calculator
This tool allows you to perform arithmetic operations on two complex numbers in the form z = a + bi, where 'a' is the real part and 'b' is the imaginary part. It supports addition, subtraction, multiplication, and division.
How to Use?
- Enter the Real and Imaginary parts for the first complex number (Z1).
- Enter the Real and Imaginary parts for the second complex number (Z2).
- Click one of the operation buttons (Add, Subtract, Multiply, Divide).
- The result will be displayed in both Rectangular (a + bi) and Polar (r ∠ θ) forms.
Features
- Four Operations: Supports standard arithmetic for complex numbers.
- Dual Output Formats: Shows results in standard (rectangular) and polar coordinates.
- Real-time Validation: Handles division by zero and invalid inputs gracefully.
FAQ
What is a Complex Number?
A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is a solution of the equation x² = −1. Because no real number satisfies this equation, 'i' is called an imaginary number.
How do you multiply complex numbers?
To multiply (a + bi) by (c + di), use the distributive property (FOIL method): <br /> (a + bi)(c + di) = ac + adi + bci + bdi² <br /> Since i² = -1, this becomes: (ac - bd) + (ad + bc)i.
What is the Polar Form?
The polar form of a complex number z = a + bi is expressed as z = r(cos θ + i sin θ), where r is the magnitude (absolute value) and θ is the argument (phase or angle).