Q:

Convert -sqrt3 - i to polar form. PLEASE HELP. Photo has more information

Accepted Solution

A:
Answer:-√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∵ [tex]r=\sqrt{x^{2}+y^{2}}[/tex]∵ x = -√3 and y = -1∴ [tex]r=\sqrt{(-\sqrt{3}) ^{2}+(-1)^{2}}=\sqrt{3+1}=\sqrt{4}=2[/tex]∵ Ф = [tex]tan^{-1}\frac{y}{x}[/tex]∴ Ф = [tex]\frac{-1}{-\sqrt{3}}=\frac{1}{\sqrt{3}}[/tex]- 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)