A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Solve.

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

    \[\frac{4+3i}{(7-2i)(5+4i)}\]

  2. barrycarter
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://www.wolframalpha.com/input/?i=%284%2B3i%29%2F%28%287-2i%29*%285%2B4i%29%29

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

    4+3i/(7-2i)(5+4i) We multiply the 2 complex numbers: And we get= 4+3i/18i + 43 From here, we can just rationalize the denominator so: We get the final answer as: -226-57i/-1867

  4. ash2326
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we have \[\frac{4+3i}{(7-2i)(5+4i)}\] multiply numerator and denominator by the conjugate of (7-2i) and (5+4i), that is (7+2i) and (5-4i) so we have \[\frac{(4+3i)(7+2i)(5-4i)}{(7-2i)(7+2i)(5-4i)(5+4i)}\] now (a+bi)(a-bi)=a^2+b^2 so we have now \[\frac{(4+3i)(7+2i)(5-4i)}{(7^2+2^2)(5^2+4^2)}\] now let's simplify the numerator by multiplying and remembering that i^2=-1 \[\frac{(28+8i+21i+6i^2)(5-4i)}{(53)(41)}\] we get now \[\frac{(28+8i+21i-6)(5-4i)}{(53)(41)}\] now we have \[\frac{(22+29i)(5-4i)}{(53)(41)}\] now multiply the other two brackets \[\frac{(110-88i+145i-116i^2)}{(53)(41)}\] now simplifying the terms and substituting i^2=-1 \[\frac{(110-116+57i)}{(53)(41)}\] we get \[\frac{(-6+57i)}{(53)(41)}\] or \[\frac{-6+57i}{2173}\]

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

    Thanks man!!!!

  6. ash2326
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry i made a mistake in the third last step it'd be \[\frac{110+116+57i}{53*41}\] so it's \[\frac{226+57i}{53*41}\] finally we get \[\frac{226+57i}{2173}\] sorry I made a mistake :(

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

    It is fine man!

  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.