PHYS 325

advertisement
PHYS 325
HW#2
F08
1. Locate the numbers z1  z 2 and z1  z 2 vectorially when
2
a) z1  2i, z 2   i b) z1  (2i), z 2  (2,0) c) z1  2  3i, z 2  2  3i
3
2. Evaluate a) 1  i 3 b) 3  4i 
1
2
c) ln 1  i  d) tan 1 1  i 
3. Derive the following trigonometric equations by using complex algebra
a) cos 3  cos 3   3 cos  sin 2 
b) sin 3  3 cos 2  sin   sin 3 
4. Show that a) i sin z  sinh iz b) sin iz  i sinh z c) cos z  cosh iz
d) cos iz  cosh z e) z n  e n ln z
5. How do circles centered on the origin in the z-plane transform for
1
w z   z 
(for z  0 ).
z
6. What part of z-plane corresponds to the interior of a unit circle in the w-plane if
z 1
w
.
z 1
7. Find the region in z-plane whose image under the transformation w  z 2 is the
rectangular domain in w-plane bounded by the lines u  1, u  2, v  1, v  2.
8. For f ( z )  z 2  1 z  2 
a) Locate the branches points.
b) Indicate two different methods of drawing branch cuts such that f(z) is single
valued in the cut plane.
Download
Related flashcards

Functional analysis

24 cards

Complex analysis

23 cards

Special functions

14 cards

Numeral systems

15 cards

Create Flashcards