1. What is Rectangular Form?

The rectangular form represents complex numbers as x + yi, where x is the real part and y is the imaginary part. This form is useful for addition, subtraction, and other algebraic operations with complex numbers.

2. How Does the Conversion Work?

The conversion from polar to rectangular form uses the formula:

Where:

• \( r \) — Magnitude (distance from origin)
• \( \theta \) — Angle in radians
• \( x \) — Real component (x = r cosθ)
• \( y \) — Imaginary component (y = r sinθ)
• \( i \) — Imaginary unit (√-1)

Explanation: The formula converts polar coordinates (magnitude and angle) to Cartesian coordinates (x and y values).

3. Importance of Complex Number Forms

Details: Different forms are useful for different operations. Polar form is better for multiplication/division, while rectangular form is better for addition/subtraction.

4. Using the Calculator

Tips: Enter magnitude (must be ≥0) and angle in radians. The calculator will output the rectangular form x + yi.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polar and rectangular forms?
A: Polar uses magnitude and angle (r, θ), while rectangular uses x and y coordinates (x + yi).

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q3: What are typical uses for rectangular form?
A: Circuit analysis, signal processing, and solving polynomial equations often use rectangular form.

Q4: Can the angle be negative?
A: Yes, negative angles represent clockwise rotation from the positive real axis.

Q5: What if I get NaN or unexpected results?
A: Check that your angle is in radians and magnitude is non-negative. Very large values may cause precision issues.