1. What is Polar to Complex Conversion?

The polar to complex conversion transforms a number from polar coordinates (magnitude and angle) to rectangular coordinates (real and imaginary parts). This is fundamental in electrical engineering, physics, and signal processing.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( a \) — Real part (unitless)
• \( b \) — Imaginary part (unitless)
• \( r \) — Magnitude (unitless)
• \( \theta \) — Angle in radians
• \( i \) — Imaginary unit (√-1)

Explanation: The real part is calculated as the magnitude times cosine of the angle, and the imaginary part as the magnitude times sine of the angle.

3. Importance of Complex Numbers

Details: Complex numbers are essential in AC circuit analysis, quantum mechanics, control theory, and many areas of engineering and physics where phase and magnitude are important.

4. Using the Calculator

Tips: Enter the magnitude (must be ≥0) and angle in radians. The calculator will output the complex number in rectangular form (a + bi).

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees?
A: Convert degrees to radians first (radians = degrees × π/180) before using this calculator.

Q2: Can I get the polar form back from the complex number?
A: Yes, use \( r = \sqrt{a^2 + b^2} \) and \( \theta = \arctan(b/a) \) (with quadrant adjustment).

Q3: What does the 'i' represent?
A: 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).

Q4: When would I use polar vs. rectangular form?
A: Polar form is better for multiplication/division, while rectangular form is better for addition/subtraction.

Q5: Are there limitations to this conversion?
A: The angle θ is periodic (2π), so multiple polar forms can represent the same complex number.