Question

How do you convert `4 (sqrt(3) +i)` to polar form?

Answer 1

`8 e^(i(pi/3))=8 ( cos (pi/6) + i sin (pi/6))`

Explanation:

`x=4sqrt3=y`
`x+ i y = r ( cos theta + i sin theta )`

`r=sqrt(x^2+y^2)=8`
`cos theta = x/r = sqrt3/2, sin theta = y/r=1/2`, Both are positive. `theta` is in the 1st quadrant.
`theta=pi/6`
So, `4( sqrt3 + i )=8 (cos pi/6 + i sin pi/6 )`