## dumbsearch2 one year ago Write z = -5 + 5i in trigonometric form.

1. dumbsearch2

2. dumbsearch2

D?

3. anonymous

|dw:1441163170659:dw|

4. surry99

Hint:Sketch the point it on the complex plane

5. dumbsearch2

I found -(pi)/(4)

6. dumbsearch2

before

7. anonymous

??

8. anonymous

|dw:1441163275849:dw|

9. dumbsearch2

What does that graph mean?

10. jim_thompson5910

-5 + 5i is in the form a+bi a = -5 b = 5 you can plot a+bi on the complex number plane as the ordered pair (a,b) which is why satellite73 plotted the point (-5,5)

11. anonymous

it means the angle is easy to find if you use arctangent here it will not work because you are in the wrong quadrant

12. jim_thompson5910
13. anonymous

if you took $$\tan^{-1}(-1)$$ you get $$-\frac{\pi}{4}$$ but you are not in quadrant 4, you are in quadrant 2

14. dumbsearch2

15. anonymous

yes

16. anonymous

you cannot use arctan unless you are in quadrant 1 or 4

17. jim_thompson5910

well you can use arctan, just add on pi to get to the right quadrant

18. dumbsearch2

?

19. anonymous

you have to either know it, or use $\cos(\theta)=\frac{a}{r}$ and $\sin(\theta)=\frac{b}{r}$

20. jim_thompson5910

as satellite73 said, arctan(-1) = -pi/4 add on pi to get to 3pi/4 (-pi/4) + (pi) = (-pi/4) + (4pi/4) = (-pi+4pi)/4 = 3pi/4

21. anonymous

or what @jim_thompson5910 said, but in any case you have to know what quadrant you are in before you start