A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find the fourth roots of the complex number z1= 1+ sqrt3 I Part 1:write z1 in polar form 2(cos60+isin60) Part 2: find the modulus of the roots of z1 I got 2 Part 3: find the four angles that define the fourth roots of the number z1 Part 4: what are the fourth roots of z1= sqrt3+1 i

  • This Question is Open
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    am I correct on part 1&2 and I don't know how to do 3&4

  2. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    .

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

    @IrishBoy123 ??

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

    If \(z\) has angle \(\theta\), then the \(n\)th roots \(z^{1/n}\) will follow a pattern of \(\dfrac{\theta+2k\pi}{n}\), where \(k=0,1,\ldots,n-1\).

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

    @SithsAndGiggles so if the angles i find are 15 and 60 the 4th roots would be \[60+2k \div4\]?

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

    Idk i just have no idea how to do this

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

    You found that \(\theta=60^\circ\), right? In radians, that's \(\dfrac{\pi}{3}\). Take \(k=0\). Then the angle of the first (principal) fourth root is \(\dfrac{\dfrac{\pi}{3}+2\pi\times0}{4}=\dfrac{\pi}{12}\), which in degrees is \(15^\circ\). Now take \(k=1\). This gives you an angle of \(\dfrac{\dfrac{\pi}{3}+2\pi\times1}{4}=\dfrac{7\pi}{12}\), or \(105^\circ\). Continue the pattern for \(k=2\) and \(k=3\).

  8. 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.