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Homework Help: Fundamentals of Complex Analysis With Applications to Engineering and Science

  1. Jan 12, 2009 #1

    CRGreathouse

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    Text: Fundamentals of Complex Analysis With Applications to Engineering and Science by E.B. Saff and A.D. Snider

    I only ordered my textbook last week (yeah... I know), so I don't think it will get to me before my homework is due. Would some kind soul with this book please post these questions? I would be very appreciative.

    1.2. #5, 6, 7, 13, 16

    Please do not help me with these questions; I prefer to work entirely on my own.
     
    Last edited: Jan 12, 2009
  2. jcsd
  3. Jan 12, 2009 #2
    I'll find the 3rd edition in my campus library tomorrow.
     
  4. Jan 13, 2009 #3
    5. Show that the points 1, [tex]-\frac{1}{2} + i \frac{\sqrt{3}}{2}[/tex] and [tex]-\frac{1}{2} - i \frac{\sqrt{3}}{2}[/tex] are the vertices of an equilateral triangle.

    6. Show that the points 3 + i, 6 and 4 + 4i are the vertices of a right triangle.

    7. Describe the set of points z in the complex plane that satisfy each of the following:
    a) Im z = -2
    b) |z - 1 + i| = 3
    c) |2z - i| = 4
    d) |z - 1| = |z + i|
    e) |z| = Re z + 2
    f) |z - 1| + |z + 1| = 7
    g) |z| = 3|z - 1|
    h) Re z [tex]\ge[/tex] 4
    i) |z - i| < 2
    j) |z| > 6

    13) Prove that if [tex](\overline{z})^2 = z^2[/tex], then z is either real or purely imaginary.

    16) Prove that if |z| = 1 (z [tex]\ne[/tex] 1), then Re[1/(1 - z)] = [tex]\frac{1}{2}[/tex].

    Good luck on your RfA (I won't vote).
     
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