Complex Number Calculator
Perform basic arithmetic operations on complex numbers. Enter real and imaginary parts to calculate.
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):
(a + bi)(c + di) = ac + adi + bci + bdi²
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).