B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 71
In what follows, open and closed means open with respect to C and closed with respect to C,
respectively; D(z, r) stands for the open disc.
1. Show that
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 61
One last word on Mbius transformations
o
1. Let C1 , C2 be two circles in C and f be a Mbius transformation given by f (z ) =
o
the image under f of C1 C
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 51
1. Find a Mbius transformation that maps the reqion outside the disc D(1 + i; 2) to
o
a) the region outside the disc D(1; 3)
b) the region dened by Rez <
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 41
1. Find the Mbius transformation f satsifying f (0) = 1, f (1 i) = i and f (2) = .
o
2. Find the Mbius transformation mapping 2, i, 0 to 1, 1, 5i, respec
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 31
1. A complex number z = x + iy may also be visualised as a 2 2 matrix
xy
y x
Verify that addition and multiplication of complex numbers dened via matrix
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 21
During this session, our main concern was to have a better understanding of the stereographic projection,
the Riemann Sphere = cfw_(1 , 2 , 3 ) R3 |1 2 +
B U Department of Mathematics
Math 232 Introduction To Complex Analysis
Spring 2008 Exercise Sheet 11
1. Express the following complex numbers in polar form.
a) z = 1 i
b) z = 3 + i
c) z = (1 i)(1 i)
3+i
d) z =
1+i
2. Prove that for any z C, |z | |Re z |