## anonymous one year ago PLEEEEEEEEEEEEEEEEEEEEEEEEEEEASE Check my answer for a medal? Express the complex number in trigonometric form. -2 + 2(square root of three)i I got 4(cos(5pi/6) + i sin(5pi/6))

1. anonymous

pls :((((

2. anonymous

The modulo of the complex number is correct

3. anonymous

okay so instead of 5pi/6 it should be 2pi/3? I'm not sure why though

4. anonymous

Correct, its 2pi/3

5. anonymous

I did arctan (2*sqrt(3) /2)

6. anonymous

To find the angle of a complex number, you apply the following formula: $\arg(z) = \frac{ \Im(z) }{ \Re(z) }$

7. anonymous

$\arg(z) = \tan^{-1} \frac{ \Im(z) }{ \Re(z) }$

8. anonymous

I missed the arctan in the previous formula.

9. anonymous

10. anonymous

arctan (2sqrt(3) / -2)?

11. anonymous

Correct.

12. anonymous

converted to radians it's (-pi/3) right? so where does the 2 come from?

13. anonymous

You will get $-\frac{ \pi }{ 3 }$

14. anonymous

Recall that you can add an angle by 2pi at any time, especially to make it positive.

15. anonymous

-pi/3 + 2pi = 5pi/3 -pi/3 - 2pi = -7pi/3??? I feel like I'm missing something obvious..:/

16. anonymous

Well, do recall that arctan, along with other inverse trig functions, is a multi-valued function.

17. anonymous

-pi/3 is only one of the possible solutions.

18. anonymous

Remember tangent is negative in both the second and fourth quadrants.

19. anonymous

I don't know how to find a value in another quadrant if it's not on the unit circle

20. anonymous

It's on the unit circle. You know that your first solution is -pi/3, which is 5pi/3 in the fourth quadrant.

21. anonymous

Your second solution must be $\pi - \frac{ \pi }{ 3 } = \frac{ 2 \pi }{ 3 }$

22. anonymous

why do you subtract it from pi?

23. anonymous

It's the unit circle. You subtract from the quadrant. You subtract from pi for the second quadrant.

24. anonymous

Oh wow. I never learned that... Thank you so much for your help!