# How do you convert from Polar to Rectangular?

Table of Contents

## How do you convert from Polar to Rectangular?

To convert from rectangular coordinates to polar coordinates, use one or more of the formulas: cosθ=xr, sinθ=yr, tanθ=yx, and r=√x2+y2.

### Can we convert polar form back into rectangular form?

Conversion between the two notational forms involves simple trigonometry. To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle.

#### How do you convert normal form to polar form?

The polar form of a complex number z = x + iy with coordinates (x, y) is given as z = r cosθ + i r sinθ = r (cosθ + i sinθ). The abbreviated polar form of a complex number is z = rcis θ, where r = √(x2 + y2) and θ = tan-1 (y/x).

What is the rectangular form of Z?

The rectangular representation of a complex number is in the form z = a + bi .

What is the polar form of z?

This can be summarized as follows: The polar form of a complex number z=a+bi is z=r(cosθ+isinθ) , where r=|z|=√a2+b2 , a=rcosθ and b=rsinθ , and θ=tan−1(ba) for a>0 and θ=tan−1(ba)+π or θ=tan−1(ba)+180° for a<0 .

## What is z in rectangular form?

The form z=a+bi is called the rectangular coordinate form of a complex number. The horizontal axis is the real axis and the vertical axis is the imaginary axis.

### How do you write z in rectangular form?

In the rectangular form, a complex number can be represented as a point on a two dimensional plane called the complex or s-plane. So for example, Z = 6 + j4 represents a single point whose coordinates represent 6 on the horizontal real axis and 4 on the vertical imaginary axis as shown.

#### What is a polar form of a complex number?

Polar Form of a Complex Number. Here are two examples of vectors and their polar notations: Vectors with polar notations. Standard orientation for vector angles in AC circuit calculations defines 0 o as being to the right (horizontal), making 90 o straight up, 180 o to the left, and 270 o straight down.

What is the difference between polar form and rectangular form?

Rectangular Form: Rectangular form is a means to represent a complex number using Cartesian coordinates i.e., x and y coordinates. Polar Form: Polar form is a means to represent a complex number using polar coordinates. The polar coordinates are {eq}r {/eq} and {eq} heta {/eq}.

How do you find the polar form of a line?

Polar Form: {eq}z=re^ {i heta} {/eq}, where {eq}r \\ge 0 {/eq} is the length of the line segment in the plane connecting the origin to the point {eq}z {/eq}.

## How do you convert a rectangle to a polar shape?

To convert from rectangular to polar, find the polar magnitude through the use of the Pythagorean Theorem (the polar magnitude is the hypotenuse of a right triangle, and the real and imaginary components are the adjacent and opposite sides, respectively), and the angle by taking the arctangent of the imaginary component divided by the real compo…