MATH CALCULATOR
Polar Form Calculator
Convert complex numbers to polar form and vice versa with this calculator.
What is the Polar Form Calculator & How does it work?
A complex number can be represented in two forms: rectangular (Cartesian) and polar. The rectangular form is given by z = a + bi, where a is the real part and b is the imaginary part. The polar form, on the other hand, represents a complex number by its magnitude (or modulus) and argument (or angle). It is expressed as z = r(cosΞΈ + i sinΞΈ), where r is the magnitude and ΞΈ is the angle in radians.
r = sqrt{a^2 + b^2}
r = magnitude of the complex number
The angle ΞΈ can be calculated using the arctangent function: ΞΈ = atan2(b, a). Conversely, to convert from polar form back to rectangular form, use the formulas: a = r cos(ΞΈ) and b = r sin(ΞΈ).
Parameters
Resultβ
Frequently Asked Questions
How do I convert a complex number to polar form?
To convert a complex number z = a + bi to polar form, calculate the magnitude r as β(aΒ² + bΒ²) and the angle ΞΈ using arctan(b/a). The polar form is then z = r(cosΞΈ + i sinΞΈ).
What is the difference between rectangular and polar forms?
Rectangular form represents a complex number as z = a + bi, where a is real and b is imaginary. Polar form expresses it by its magnitude r and angle ΞΈ as z = r(cosΞΈ + i sinΞΈ).
Can you explain how to find the magnitude of a complex number?
The magnitude (or modulus) of a complex number z = a + bi is calculated using the formula r = β(aΒ² + bΒ²).
How do I calculate the angle ΞΈ in polar form?
The angle ΞΈ can be found using the arctangent function: ΞΈ = arctan(b/a), where a is the real part and b is the imaginary part of the complex number.
What are some practical applications of polar form in mathematics?
Polar form is useful for simplifying multiplication and division of complex numbers, analyzing AC circuits in electrical engineering, and representing periodic functions in physics.
Results are for informational purposes only and do not constitute professional advice.