A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

evaluate the radical expression and express the result in a+bi form

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

    \[(3-\sqrt{-5}) (1+\sqrt{-1})\]

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

    well you need to distribute so it is \[3(1 + \sqrt{-1})-\sqrt{-5}(1 + \sqrt{-1})\] what do you think the next line of working is..?

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

    \[3(1+i)-i \sqrt{5}(1+i)\]

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

    ?

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

    good, now distribute the 3, and the -i√5

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

    \[(3+3i)(-i \sqrt{5}+1\sqrt{5}) ?\]

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

    \[(3-\sqrt{-5}) (1+\sqrt{-1}) \] \[(3-\sqrt{5}i) (1+i)\] now expand.

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

    all negatives in the radical should be pulled out first.. so that square root of -5 should be square root of 5 i

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

    \[3(1+i)-i \sqrt{5}(1+i)\\=(3+3i)+(-i \sqrt{5}-\sqrt{5}i\times i) \]

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

    \[(3-\sqrt{5}i) (1+i) \] \[3+3i-\sqrt{5}i-\sqrt{5}(i)(i)\] note \[i^2 = -1 \]

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

    typed too fast... -1 inside the square root is just an i

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

    \[(3+\sqrt{5})+(3-\sqrt{5})i\]

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

    is that right?

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

    hold on.

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

    \[3+3i-\sqrt{5}i-\sqrt{5}(-1)\] \[3+3i-\sqrt{5}i+\sqrt{5}\] \[3+\sqrt{5}+3i-\sqrt{5}i\] \[\[3+\sqrt{5}+i(3-\sqrt{5})\]\] yeah it's correct

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

    my i is placed differently, but it shouldn't matter because we still have a+bi only our a =\[3+\sqrt{5}\] and b = \[3-\sqrt{5}\]

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

    thank you so much!

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

    it's best to convert all negatives in the square root to i's first and if it's a perfect square like \[\sqrt{-1} \] just take the square root and add an i \[\sqrt{-1} \rightarrow i \] similarly for \[\sqrt{-5} \rightarrow \sqrt{5}i\]

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

    but 5 isn't a perfect square so leave it in the radical and only the negative pops out of the radical and becomes i

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

    negatives inside the radical produce imaginary results.

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

    then use foil and i^2 = -1 ... simplify until a+bi or ai+b form is achieved.

  22. 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.