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Pre calculus, help i CANT solve this problems

  1. Oct 15, 2007 #1
    hello! Im a studen from sweden and i having some troble solves this kind of problems. i have tried but the book its really bad to expleain. and i really have to know this for the comming exan, so if anyone could help me i really be so happy :)

    here are some stuff i have hard time solving:

    1) z^4=16i
    2) 2z³ - 3z² + 2z -3 = 0


    thnx again for any help
     
  2. jcsd
  3. Oct 15, 2007 #2
    are those 2 separate problems or do i solve for 1 and apply it to 2?

    1 - clarify question or how do you get an imaginary number?

    [tex]\sqrt{-X}=\sqrt{X}i[/tex]

    2 - factor out a common term, hint z^2
     
  4. Oct 15, 2007 #3
    there are 2 separate problems.

    the first one its so hard i dont where to start. or how to solve it

    and the second one ill start to factor out term z² and see what happens thnx.
     
  5. Oct 15, 2007 #4
    i cant factor out 2² in 2)

    because : 2z³ - 3z² + 2z -3 = 0 has 2z so its not and z² type.
    what to do?
     
  6. Oct 15, 2007 #5
    not 2^2 but z^2, you eventually get

    [tex]z^{2}(2z-3)+(2z-3)=0[/tex]

    what would your next step be?
     
  7. Oct 15, 2007 #6
    that would be maybe

    z² = - (2z - 3)/(2z - 3)
    z² = -1

    its that right?
     
  8. Oct 15, 2007 #7
    [tex]z^{2}(2z-3)+(2z-3)=0[/tex]

    there is an implied one infront of the 2nd parenthesis

    so

    [tex]z^{2}(2z-3)+1(2z-3)=0[/tex]

    pull out a common term of 2z-3

    [tex](z^{2}+1)(2z-3)=0[/tex]

    yes?
     
  9. Oct 17, 2007 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you know how to put a complex number in "polar form"?

    Do you know DeMoivre's theorem? Those are necessary for problem 1.
     
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