A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jiteshmeghwal9

  • one year ago

If\[z_1=2+3i\]\[z_2=1+2i\]then \[z_1z_2-z_1^3=?\]

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

    Give it your best try and show your steps

  2. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[z_1.z_2=(2+3i)(1+2i)\]\[z_1z_2=(2-6)+i(4+3)\]\[z_1z_2=-4+7i\]now\[z_1^3=8+27i^3+54i^2+36i\]\[z_1^3=-46+27i^3+36i\]\[z_1z_2-z_1^3=42-29i+27i^3\]

  3. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now wht next ?

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Nice! \(i^3\) simplifies further right ?

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

    It looks almost right, except you seem to have messed up your terms here: \(z_1^3 = 8 + 12i + 18i^2 + 27i^3\) Which can also be simplified further with @ganeshie8 's comment. :D

  6. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(42-29i-27i\)=\(42-56i\)

  7. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1440491573056:dw|

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

    The picture is nice since all a cube power means is multiply something by itself three times, \(i^3 = i*i*i\) So simplifying this should be no big deal, since you know what \(i*i=-1\) already.

  9. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the answer given in book is \(42-2i\). nt matching :/

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.wolframalpha.com/input/?i=%282%2B3i%29*%281%2B2i%29-%282%2B3i%29%5E3

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    must be an algebra error somewhere, just double check..

  12. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes\[z_1z_2-z_1^3=42-29i-27i^3\]\[=42-29i+27i=42-2i\]

  13. jiteshmeghwal9
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanx

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    In case this is first time, it might be a bit exciting to notice that any power of \(i\) always simplifies to one of the numbers : \(\{\pm 1, ~\pm i\}\)

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    This holds : \[\large i^{n}\equiv i^{n\pmod{4}}\] In other words, subtracting/adding \(4\) from the exponent doesn't change the number

  16. 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.