A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Express the complex number in trigonometric form. -3i

  • This Question is Closed
  1. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    r = √0^2 + -3^2 = √0 + 9 = √9 = 3

  4. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yep `r = 3`

  5. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what would theta be?

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im getting an error for theta..

  8. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cos(x) = 0 ?

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  11. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    270 ?

  13. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  15. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1442705859091:dw|

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3(cos 270 + i sin 270) ?

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    correct

  18. Plasmataco
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yay

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.