If (a,b) is a are the coordinates of a point in Cartesian Plane, u is its magnitude and alpha is its angle then (a,b) in Polar Form is written as (u,alpha).
Magnitude of a cartesian coordinates (a,b) is given bysqrt(a^2+b^2) and its angle is given by tan^-1(b/a)
Let r be the magnitude of (1,-sqrt3) and theta be its angle.
Magnitude of (1,-sqrt3)=sqrt((1)^2+(-sqrt3)^2)=sqrt(1+3)=sqrt4=2=r
Angle of (1,-sqrt3)=Tan^-1(-sqrt3/1)=Tan^-1(-sqrt3)=-pi/3
implies Angle of (1,-sqrt3)=-pi/3
But since the point is in fourth quadrant so we have to add 2pi which will give us the angle.
implies Angle of (1,-sqrt3)=-pi/3+2pi=(-pi+6pi)/3=(5pi)/3
implies Angle of (1,-sqrt3)=(5pi)/3=theta
implies (1,-sqrt3)=(r,theta)=(2,(5pi)/3)
implies (1,-sqrt3)=(2,(5pi)/3)
Note that the angle is given in radian measure.
Note that the answer (1,-sqrt3)=(2,-pi/3) is also correct.
