## anonymous one year ago Can someone please help me finish this pre-calc question??? Express the complex number in trigonometric form. 2 - 2i This is what I have so far: r=absolute value(2-2i) r= sqrt((2)^2+(-2)^2) r=sqrt(8) r=2sqrt(2) theta(ref)=tan^-1*absolute value(2/-2) theta(ref)=pi/2 I dont know how to get the value of theta alone to complete this problem. What do i do next? Please help!

1. anonymous

$2-2i$$r=\sqrt{2^2+(-2)^2}$$\tan^{-1} = (\frac{ -2 }{ 2 } ) = ?$

2. anonymous

you arent suppose to use radian mode for polar form

3. anonymous

thats why you got pi/2

4. anonymous

I thought $\tan^{-1} =\frac{ a }{ b }$

5. anonymous

no its b/a

6. anonymous

|dw:1439092982007:dw|

7. anonymous

better if i draw it out?

8. anonymous

Yes. After switching it to b/a i got theta(ref)=-1

9. anonymous

find out whats tan^1(-1)

10. anonymous

tan^1(-1) or tan^-1(1)? tan^1(-1) is -1.55 or -tan(1) http://www.wolframalpha.com/input/?i=tan%5E1%28-1%29

11. anonymous

$\tan^{-1} (-1)$

12. anonymous

Okay, yeah tan^-1(-1) is -pi/4 or -45 degrees

13. anonymous

now put that in 360 degrees form

14. anonymous

find the angle that is coterminal to -45 degrees? Thats 315, right?

15. anonymous

yea

16. anonymous

you know how to make the polar form from there right?

17. anonymous

oh wait its trigo form

18. anonymous

Yea. I was stuck at theta(ref)= -1. I dont know what to do next

19. anonymous

ok great you have the angles now you can form whatever it is

20. anonymous

you should get $$\theta$$ instantly from your eyeballs