Polar Form of a Complex Number
Polar Form Representation of a Complex Number
The Polar Form of a complex number is written in terms of its magnitude and angle. Thus, a polar form vector is presented as:
z= r ∠±, where: z is the complex number in polar form, r is the magnitude or modulo of the vector and is its angle or argument of r. T
In polar form the location of the point is represented in a “triangular form” as shown below.
Converting between Rectangular Form and Polar Form
We can use simple geometry of the triangle and especially trigonometry and Pythagoras’s Theorem on triangles to find both the magnitude and the angle of the complex number. As we remember from school, trigonometry deals with the relationship between the sides and the angles of triangles so we can describe the relationships between the sides as: