anonymous one year ago Extremely quick question! Thank You! Is w=-2-2i in polar form 2sqrt(2)(cos(pi/4)+isin(pi/4))?

1. anonymous

@Ashleyisakitty @satellite73 @jim_thompson5910 @campbell_st @zepdrix @TheSmartOne @Nnesha @Luigi0210 @Compassionate

2. anonymous

I'm worried theta might be wrong

3. zepdrix

hmm ya, it can't be pi/4 right? we're in quadrant three if both the real and imaginary part are negative.

4. anonymous

-2/-2=1 So I thought that was why. Is there a rule I don't know?

5. zepdrix

Well, when you apply your arctangent (im assuming that's what you're doing),$\Large\rm \arctan\left(\frac{-2}{-2}\right)=\theta$Yes, you end up with pi/4 as a reference angle. But this really corresponds to two angles in one full rotation. You have to look back at your rectangular form to see where you should be.

6. zepdrix

Since they're both negative, we need the NEXT angle, which will be pi/4 + pi

7. anonymous

Oh, I see what you mean.

8. anonymous

5pi/4?

9. anonymous

not to butt in, but drawing a picture is real helpful by which i only mean "plot the point"

10. zepdrix

ya 5pi/4 sounds better :)

11. anonymous

Oh, gotcha @satellite73

12. anonymous

it will keep you from doing something silly like taking $\tan^{-1}(\frac{b}{a})$ which does not really work

13. anonymous

@satellite73 yup, I'll do that next time.

14. anonymous

Thanks for the help everyone :D