Polar Form Calculator

The Polar Form Calculator converts rectangular coordinates (real and imaginary parts) into polar form by calculating the magnitude and angle in both radians and degrees.

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Step-by-Step Guide to Using the Polar Form Calculator

Introduction

The Polar Form Calculator is a tool designed to help you convert rectangular coordinates into polar coordinates. It calculates the magnitude and angle of a complex number from its real and imaginary parts.

Inputting Data

  1. Enter the Real Part (x): Begin by inputting the real part of the complex number into the field labeled “Real Part (x)”. Make sure that the value you enter is a number between -1,000,000 and 1,000,000, rounded to four decimal places.

  2. Enter the Imaginary Part (y): Next, input the imaginary part into the field labeled “Imaginary Part (y)”. This value should also be a number between -1,000,000 and 1,000,000 with four decimal place precision.

Understanding the Results

Once you have input the real and imaginary parts, the calculator will automatically compute the corresponding polar coordinates and present them in the result fields.

  1. Magnitude (r): The magnitude is calculated using the formula √(x2 + y2). This value represents the distance of the point from the origin and it will be rounded to four decimal places.

  2. Angle (θ) in Radians: The angle in radians is determined using the atan2(y, x) function, which calculates the arctangent while considering the signs of both arguments to determine the right quadrant. The result will be displayed with a suffix “rad” and rounded to four decimal places.

  3. Angle (θ) in Degrees: Similarly, the angle in degrees is calculated by converting the radians into degrees using the formula θ * 180 / π. The value is rounded and displayed with a degree symbol.

  4. Polar Form: Finally, the polar form is expressed using the formula “r ∠ θ°”, where r is the magnitude and θ is the angle in degrees. This provides a compact and intuitive representation of the complex number in polar coordinates.

Conclusion

By following these steps, users can effortlessly convert complex numbers from rectangular to polar form, gaining insight into their magnitude and direction. This calculator is useful in various mathematical and engineering applications where such conversions are necessary.