Complex Analysis

Math 312 Spring 1998  MWF 10:30am-11:25am
Buckmire  Fowler 112

Worksheet �1 (Monday 01/12/98)

SUMMARY What do we know about complex numbers so far? Here is a list of properties and operations we know about to date. Make sure you understand how each one works.

Consider 2 complex numbers z = x + iy and p = a + ib

• EQUALITY

• CONJUGATE

• MODULUS (absolute value)

• ADDITION

• MULTIPLICATION

• DIVISION

Exercise With your nearest neighbor compute the value of the expressions A and B so that they are complex numbers of the form x + iy.

A = \frac{3 + 2i + (−2 + i)}{3 − 4i}, B = (\frac{6}{5} + 2i − (3 − \frac{3}{5}i))

Then answer the following questions:

(a) Is A = B?

(b) Which is bigger, A or B?

From this example write down one signi�cant difference between the set of real numbers and the set of complex numbers: