Question

How do you convert `-7-7sqrt3i` to polar form?

Answer 1

`(14,(4pi)/3)`

Explanation:

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

`"that is "x+yito(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=-7" and "y=-7sqrt3`

`rArrr=sqrt((-7)^2+(-7sqrt3)^2)`

`color(white)(rArrr)=sqrt(49+147)=sqrt196=14`

`"since "-7-7sqrt3i" is in the third quadrant we must"`
`"ensure that "theta" is in the third quadrant"`

`theta=tan^-1(sqrt3)=pi/3larrcolor(blue)"related acute angle"`

`rArrtheta=(pi+pi/3)=(4pi)/3larrcolor(blue)" in third quadrant"`

`rArr(-7,-7sqrt3)to(14,(4pi)/3)`