Fundamentals of Complex Analysis With Applications to Engineering and Science

[CRGreathouse]

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.

 

[mutton]

I'll find the 3rd edition in my campus library tomorrow.

 

[mutton]

5. Show that the points 1, $$-\frac{1}{2} + i \frac{\sqrt{3}}{2}$$ and $$-\frac{1}{2} - i \frac{\sqrt{3}}{2}$$ 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) I am 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 $$\ge$$ 4
i) |z - i| < 2
j) |z| > 6

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

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

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