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.