## How do you convert to polar form?

To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

- r = √ ( x2 + y2 )
- θ = tan-1 ( y / x )

**What is the polar form of − 3i?**

Polar Form of Complex Number/Examples/-3i The complex number −3i can be expressed as a complex number in polar form as ⟨3,3π2⟩.

**How do you convert 6i to polar form?**

1 Answer

- A complex number a+ib in polar form is written as.
- rcosθ+irsinθ
- Hence r=√a2+b2.
- As −6i can be written as 0−6i.
- r=√2+(−6)2)=√36=6 and hence.
- Hence, θ=−π2 and.
- Polar form of −6i is (6,−π2)

### What is the polar form of I?

So, the polar form is. ∴i=rcosθ+irsinθ=cos2π+isin2π

**What is the polar form of 0 i?**

By convention we choose (0,0) as the polar origin, or “pole”.

**How do you write 5 5i in polar form?**

Polar Form of Complex Number/Examples/-5 + 5i The complex number −5+5i can be expressed as a complex number in polar form as ⟨5√2,3π4⟩.

#### What is the argument of 2 2i?

The argument of -2 -2i is either the negative angle from the positive real axis clockwise to the radial line, or the positive angle from the positive real axis counterclockwise to the radial line.

**Why do we use polar form?**

Applications. Polar coordinates are two-dimensional and thus they can be used only where point positions lie on a single two-dimensional plane. They are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point.

**Which is the polar form of 7-5i?**

Hence, the polar form of 7-5i is represented by: Suppose we have two complex numbers, one in a rectangular form and one in polar form. Now, we need to add these two numbers and represent in the polar form again. Let 3+5i, and 7∠50° are the two complex numbers. First, we will convert 7∠50° into a rectangular form.

## How to write the complex number-2i in polar form?

Because the real part (a) of the complex number is zero, you cannot use θ = tan−1(b a); you must know that the angle is either π 2 or 3 π 2. Because the sign of the complex part is negative, you must know that this makes the angle the latter, 3 π 2. You can see that the magnitude is 2.

**How do you convert 3i to polar form?**

A complex number takes the form #z=a+bi#. In this example, #a=0# and #b=3# because #z=0+3i#. To find #r#, use the pythagorean theorem. #r=sqrt(a^2 +b^2)#. To find #theta#, think about #a# as a value along the x-axis, and #b# as a value along the y axis. In this case, #a# is zero.

**Which is an example of a polar number?**

Let us see some examples of conversion of the rectangular form of complex numbers into polar form. Example: Find the polar form of complex number 7-5i. Solution:7-5i is the rectangular form of a complex number.