1. What is Rectangular Form?

The rectangular form (also called Cartesian form) is a way to represent complex numbers using real and imaginary components. It's expressed as z = x + yi, where x is the real part and y is the imaginary part.

2. How Does the Calculator Work?

The calculator simply combines the real and imaginary parts you provide into the standard rectangular form:

Where:

• \( x \) — Real part (unitless)
• \( y \) — Imaginary part (unitless)
• \( i \) — Imaginary unit (√-1)

Explanation: The calculator formats the input values properly, handling cases where coefficients are 1, -1, or 0 for clean mathematical representation.

3. Importance of Rectangular Form

Details: Rectangular form is essential for complex number arithmetic (addition, subtraction) and is widely used in engineering, physics, and mathematics for representing complex quantities.

4. Using the Calculator

Tips: Enter the real part (x) and imaginary part (y) of your complex number. The calculator will automatically format it into proper rectangular form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between rectangular and polar form?
A: Rectangular form uses x + yi while polar form uses magnitude and angle (r∠θ). Each is better suited for different operations.

Q2: How do I add complex numbers in rectangular form?
A: Simply add the real parts and imaginary parts separately: (a+bi) + (c+di) = (a+c)+(b+d)i.

Q3: Can I represent pure real or imaginary numbers?
A: Yes, for pure real set y=0 (e.g., 5+0i = 5). For pure imaginary set x=0 (e.g., 0+3i = 3i).

Q4: What's the complex conjugate?
A: For x+yi, the conjugate is x-yi. It's useful for division of complex numbers.

Q5: How do I convert to polar form?
A: Magnitude r = √(x²+y²), angle θ = atan2(y,x). Our polar form calculator can help with this conversion.