1. Not finding help here? Sign up for a free 30min 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!

Complex Analysis

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data

    1- Find the two square roots of the complex number z=3+4i.

    2a- Solve in ℂ the equations: (E): 4z^2-10iz-7-i=0

    b- Let a and b be solutions to (E) such that: Re(a)<0 and the two points A and B plots/pictures of a and b. Show that b/a=1-i. Conclude that AOB is an equilateral triangle.

    3. The attempt at a solution

    1- After solving (p+qi)^2=3+4i i found that the solutions were either 2+i or -2-i.

    2-a For the complex equation i found two complex roots: z1=(-3+6i)/8 and z2=(3+14i)/8.

    b- So i took the two solutions that i found from the previous question and chose a=z1 and b=z2 and after computing i got a whole different answer. Is my work correct, if not some help would be very much appreciated.
     
  2. jcsd
  3. Feb 8, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I get a different result. Pls post your working.
     
  4. Feb 8, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If z= (-3+ 6i)/8 then [itex]z^2= [(9- 36)- 2(18i)]/64= -27/64- (9/8)i[/itex] so [itex]4z^2- 10iz- 7- i= -27/4- (9/2)i+ (15/4)i+ 15/2- 7- i= (-27/4+ 15/2- 7)+ (15/4- 9/2- 1)i= (-27+ 30- 28)/4+ (15/4- 18/4- 4/4)i= -25/4- (7/4)i, NOT 0.

     
  5. Feb 8, 2013 #4
    Sorry I was wrong on the roots of the equation they are correct now i got:

    z1=(1/2)+(3i/2) and z2=(-1/2)+i and that certainly gives 1-i when you take z2=a and z1=b.

    But the conclusion i can't quite fathom, any help with that please.
     
  6. Feb 8, 2013 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    What will the third side look like as a complex number (in terms of a and b)? What will its ratios be to the other two?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex Analysis
  1. Complex analysis (Replies: 3)

  2. Complex Analysis (Replies: 18)

  3. Complex Analysis (Replies: 0)

  4. Complex Analysis (Replies: 4)

  5. Complex analysis (Replies: 10)

Loading...