Convert Rectangular Equation To Polar

Scheme

The two sine waves A and B (B leads A by φ = twenty°) are represented by a phasor diagram, in which sine wave A has a larger amplitude than sine wave B as indicated by the length of their phasors.

This Cartesian-polar (rectangular–polar) phasor conversion calculator tin can convert complex numbers in the rectangular form to their equivalent value in polar form and vice versa.

Case 1: Convert an impedance in rectangular (complex) form Z = 5 + j2 Ω to polar form.

Example 2: Catechumen a voltage in polar form U = 206 ∠120° V to rectangular (complex) course.

Polar to Rectangular

Radius

Angle

∠φ

To calculate, select degrees or radians, enter the radius and bending and click or tap the Convert push button.

Rectangular to Polar

Complex number

To calculate, enter the real and imaginary parts and click or tap the Convert button.

Definitions and Formulas

In electric engineering and electronics, when dealing with frequency-dependent sinusoidal sources and reactive loads, we demand not only real numbers, but too circuitous numbers to be able to solve complex equations. Complex numbers allow mathematical operators with phasors and are very useful in the analysis of Ac circuits with sinusoidal currents and voltages. Using complex numbers, we can practice four arithmetic operations with quantities that accept both magnitude and angle, and sinusoidal voltages and other Air conditioning excursion quantities are precisely characterized by amplitude and angle. See our Electric, RF and Electronics calculators and Electrical Engineering Converters.

A complex number z can be expressed in the class z = x + jy where x and y are existent numbers and j is the imaginary unit commonly known in electric technology as the j-operator that is divers by the equation j² = –1. In a complex number x + jy, x is chosen the existent part and y is called the imaginary office. We utilize the alphabetic character j in electric engineering considering the letter i is reserved for instantaneous current. In math, the letter of the alphabet i is used instead of j.

A complex number z = 10 + jy = r ∠φ is represented every bit a point and a vector in the complex plane

Complex numbers can be visually represented as a vector on the complex plane, which is a modified Cartesian plane, where the horizontal centrality is chosen the real axis Re and displays the real part and the vertical axis is called the imaginary axis Im and displays the imaginary role. Any complex number tin can be represented past a displacement along the horizontal axis (real part) and a displacement along the vertical axis (imaginary part).

A circuitous number can besides exist represented on the complex plane in the polar coordinate system. The polar representation consists of the vector magnitude r and its angular position φ relative to the reference axis 0° expressed in the post-obit form:

Formula

In electrical engineering and electronics, a phasor (from phase vector) is a complex number in the form of a vector in the polar coordinate organization representing a sinusoidal function that varies with fourth dimension. The length of the phasor vector represents the magnitude of a function and the angle φ represents the angular position of the vector. Positive angles are measured counterclockwise from the reference axis 0° and negative angles are measured clockwise from the reference centrality.

As the polar representation of a complex number is based on a correct-angled triangle, nosotros can use the Pythagorean theorem to find both the magnitude and the bending of a complex number, which is described below.

To convert from Cartesian coordinates x, y to polar coordinates r, φ, apply the post-obit formulas:

Formula

If these formulas are used in electrical applied science calculations (see our Ac Ability Estimator and Three-Stage AC Power Calculator), so x is always positive and y is positive for an inductive load (lagging current) and negative for a capacitive load (leading electric current). In this case, for capacitive loads, the angles should be negative in the range of –90° ≤ φ ≤ 0 and should not be corrected equally described in the to a higher place formulas (that is, 360° is not added).

To catechumen from polar coordinates r, φ to Cartesian coordinates 10, y, practice the following:

Formula