Convert (5, π/3) from (r, θ) to different polar forms.

Question

1. (r, -θ) =
2. (-r, θ) =
3. (-r, -θ) =

Answer 1

-Θ just means measuring clockwise in the plane around the origin, so (5 , - π /3) could also be expressed as

(5 , 5π /3) , if you need to express Θ as an angle such that 0 ≤ Θ < 2π. (We add 2π to the negative angle.)

-r means travel r units in the direction opposite to Θ, i.e. Θ + π or Θ - π , depending on the angle.

So we can rewrite (-5 , π /3) as (5 , 4π/3) if we need to express it with a positive radius.

Likewise, (-5 , - π /3) = (5 , 2π /3).

Btw these 4 complex #s are 5/2 + 5√3/2 i , 5/2 - 5√3/2 i, - 5/2 - 5√3/2 i, and - 5/2 + 5√3/2 i in rectangular form.