Convert -sqrt3 - i to polar form. . photo has more information

-√3 - i ⇒ (2 , 7/6 π)

Step-by-step explanation:

* Lets explain how to convert a point in Cartesian form to polar form

- Polar coordinates of a point is (r , θ).

- The origin is called the pole, and the x axis is called the polar axis,

 because every angle is dependent on it.

- The angle measurement θ can be expressed in radians or degrees.

- To convert from Cartesian Coordinates (x , y) to Polar

 Coordinates (r , θ)

1. r = √( x² + y² )

2. θ = tan^-1 (y/x)

* Lets solve the problem

∵ The point in the Cartesian form is z = -√3 - i, where -√3 is the real

   part and -i is the imaginary part

∴ The x-coordinate of the point is -√3

∴ The y-coordinate of the point is -1

∵ Both the coordinates are negative

∴ The point lies on the 3rd quadrant

- To convert it to the polar form find r and Ф

∵

∵ x = -√3 and y = -1

∴

∵ Ф =

∴ Ф =

- The acute angle π/6 has tan^-1 (1/√3)

∵ The point is in the third quadrant

∴ Ф = π + π/6 = 7/6 π

- Lets write it in the polar form

∴ -√3 - i ⇒ (2 , 7/6 π)

answerthe vertex form

step-by-step explanation:

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