1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: QUICK HELP complex numbers

  1. Nov 23, 2004 #1
    Let Z1 = 3-i
    Z2=7+2i express (1/Z1)-(1/Z2) in form a+bi
    SOMEONE plzzzzzzz HELP ME!!! I dont have a clue as to how to do this :cry:
    What do I do?
    Where do I start? :cry:
  2. jcsd
  3. Nov 23, 2004 #2
    Have you ever rationalized the denominator of a fraction before? This is pretty much the same thing. For instance, when you have a fraction such as [tex]\frac{5}{\sqrt{3}+2}[/tex], you multiply the top and bottom by the conjugate, because you know a difference of squares will result in a rational number, because the square root of a rational squared is a rational. The same idea applies here: just keep in mind that [tex]i=\sqrt{-1}[/tex], and apply the same concept.

    Hope that helps! :)
  4. Nov 23, 2004 #3
    Do you know what a "complex conjugate" is?
  5. Nov 23, 2004 #4
    Yes I do it is the opposite sign well when dividing you take the denominator and divide by the conjugate I know that but in this question I dont know what to do or what order to do it in plz help me plzzz
  6. Nov 23, 2004 #5


    User Avatar
    Science Advisor
    Homework Helper

    nolachrymose described it pretty well.

    If you substituted i for the square root of 3,


    and multiplied by the conjugate, you'd get:

    [tex]\frac{5(\sqrt{-1}-2)}{-1 - 4} = 2 - \sqrt{-1}[/tex]

    The i is square root of negative one. If you have 3i and square it, you get -9. Other than keeping the negative signs straight, it's just like working with a square root.
  7. Nov 23, 2004 #6
    Ive never rationalized the denominator of a fraction :frown: so im a little lost I tried multiplying 1/3-i first by the conjugate and got the answer of 3+i/10 and then i did the same for z2 and got 7-2i/53 but if i subtract the two i dont get the right answer plz show me how do i divide first subtract use conjugates or what?
  8. Nov 23, 2004 #7
    As far as I can tell you rationalized the two properly. Unless you made a subtraction error, your answer should be right. What did you get as the final answer?
  9. Nov 23, 2004 #8
    There are 4 possible answers




    I dont get anything close to these when i take those two answers and subtract them. Please help me Ive been doing this one forever :mad:
  10. Nov 24, 2004 #9


    User Avatar
    Science Advisor
    Homework Helper

    All of their choices are wrong.

    So what did you get? Something close to

  11. Nov 24, 2004 #10


    User Avatar
    Science Advisor
    Homework Helper

    I think I know where they made their mistake. You can do this two ways.












    [tex]\frac{(92+(-3))+(69i+4i)}{529-(-1)}[/tex] Here's where they made their mistake


    You can break this up into two separate fractions, if you want:


    Instead of multiplying (23-i)(23+i) and getting 529+1, they got 23+1. So, the answer they most likely picked is (b)
  12. Nov 24, 2004 #11


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    A great example of why multiple choice exams are (IMO) inferior to some other exam types which are less sensitive to designer flaws.
  13. Nov 24, 2004 #12


    User Avatar
    Science Advisor
    Homework Helper

    A flaw?! Or is it really a hidden 'feature'? :devil: (how come we don't have a 'shifty eyed' smilie?)

    "B's for everyone who answers all the questions right. A's for everyone who catches my error and figures out exactly where I made my mistake!"
  14. Nov 24, 2004 #13
    Well my answer was (89-33i)/530
    u are right that the question that was correct was b with the error in it. I think our answers are different because when u expanded -10(7-2i)/530 u wrote -70-20i shouldnt this be -70+2i because of the two negative signs? I will for sure point this question out to my teacher maybe she will give me an "A" lol for cathching the errors. Thanks so much I thought I was doing this totally wrong, but I guess not thanks again ur my HERO :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook