anonymous one year ago Express the complex number in trigonometric form. -2 + 2square root of threei

1. anonymous

@mathmath333

2. anonymous

@dan815

3. anonymous

SOMEONE HELP

4. amistre64

what 2 things do we need to determine for the trig form?

5. anonymous

the absolute value? @amistre64

6. amistre64

hmm, i was thinking a radius and an angle

7. anonymous

oh sorry, I have no idea how to do this

8. amistre64

spose we plot some point (x,y) define as some complex number: x + iy |dw:1440473957824:dw| we can then determine the distance from the origin, and the angle the ray makes with the x axis

9. amistre64

r = sqrt(x^2+y^2) a = tan^(-1) (y/x)

10. anonymous

okay so I plug the numbers into that formula?

11. amistre64

what else would you do with a formula? trig defines x = r cos(a) and y=r sin(a) therefore our trig form of a complex number is: x + iy to r cos(a) + r i sin(a) or simplified to: r (cos(a) + i sin(a))

12. anonymous

4(cos5pi/6+isin5pi/6)?

13. anonymous

?

14. amistre64

$\Large \underbrace{-2}_x+i~\underbrace{2\sqrt3}_y$ $r=\sqrt{x^2+y^2}=\sqrt{4+12}=4~;~is~fine$ $\alpha=tan^{-1}(-\frac{1}{\sqrt3})=30^o~(Q2)$

15. amistre64

yeah, looks good to me in my head lol

16. amistre64

|dw:1440474530757:dw|

17. anonymous

Okay, thank you!

18. amistre64

youre welcome