## anonymous one year ago Express the complex number in trigonometric form. -3i

1. jim_thompson5910

Think of -3i as 0-3i = 0 + (-3i) the last expression is in the form a+bi where a = 0 and b = -3

2. jim_thompson5910

You need to find r and theta use $\Large r = \sqrt{a^2 + b^2}$ $\Large \theta = \arctan\left(\frac{b}{a}\right)$

3. anonymous

r = √0^2 + -3^2 = √0 + 9 = √9 = 3

4. jim_thompson5910

yep r = 3

5. jim_thompson5910

basically that says: "the point (0,-3) is 3 units away from the origin" 0+(-3i) can be plotted on the complex plane as the point (0,-3)

6. jim_thompson5910

what would theta be?

7. anonymous

im getting an error for theta..

8. jim_thompson5910

yes you'll find that b/a = -3/0 = undefined where is tangent undefined?

9. anonymous

cos(x) = 0 ?

10. jim_thompson5910

I guess a better way to find theta is by plotting where 0-3i is located |dw:1442705686511:dw|

11. jim_thompson5910

what angle is this? |dw:1442705720789:dw|

12. anonymous

270 ?

13. jim_thompson5910

yes

14. jim_thompson5910

r = 3 and theta = 270, we now plug those values into $\Large r\left[\cos(\theta)+i*\sin(\theta)\right]$

15. jim_thompson5910

|dw:1442705859091:dw|

16. anonymous

3(cos 270 + i sin 270) ?

17. jim_thompson5910

correct

18. Plasmataco

yay