Question

How do you convert `8 - 15i` to polar form?

Answer 1

`(17,-1.08)`

Explanation:

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

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

`• r=sqrt(x^2+y^2)`

`• theta=tan^-1(y/x); -pi < theta <= pi`

`"here " (x,y)=(8,-15)`

`rArrr=sqrt(8^2+(-15)^2)=17`

`"now " 8-15i" is in the fourth quadrant so we must ensure"`
`"that "theta" is in the fourth quadrant"`

`theta=tan^-1(-15/8)=-1.08larrcolor(red)" in fourth quadrant"`

`rArr8-15ito(17,-1.08)`