Question

How do you convert `(1, sqrt3)` into polar form?

Answer 1

`2_(pi/3)`

See below

Explanation:

The pole `rho` is the module of complex number `z=1+sqrt3i`. So

`rho=sqrt(1+3)=2`

`theta=arctan(sqrt3/1)=60º=pi/3`.

Answer 2

`(2,pi/3)`

Explanation:

`"to convert from "color(blue)"cartesian to polar form"`

`"that is " (x,y)to(r,theta)" using"`

`•color(white)(x)r=sqrt(x^2+y^2)`

`•color(white)(x)theta=tan^-1(y/x)`

`"here "x=1" and "y=sqrt3`

`rArrr=sqrt(1^2+(sqrt3)^2)=2`

`rArrtheta=tan^-1(sqrt3)=pi/3`

`rArr(1,sqrt3)to(2,pi/3)`