*Exam
1 will be Thursday, March 13, 2008.*
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Possible problems include (but are not
limited to):
·
Prove that a number is irrational. (2.1.1)
·
By analyzing the denominator, determine
whether a rational number will have a decimal representation that is
terminating, simple-periodic, or delayed-periodic. If it is terminating, find the number of
decimal places after which the representation terminates. If it is periodic, find the maximum period
and the length of the delay. Be able to
explain your answers in any case. (2.1.3)
·
Find a repeating decimal representation
for a rational number (by hand or with calculator and division algorithm). (Calculator: 2.1.3, #3)
·
Prove that a
number is algebraic. (2.1.4, # 3, 4, 5)
·
Show that two sets have the same
cardinality. (2.1.4, e.g., #8)
·
Write complex numbers in 5 different
forms; find |z|, Arg(z), Re(z), Im(z). (2.2.1, 2.2.2)
·
Perform operations on complex numbers
(add, subtract, multiply, divide, powers).
(2.2.1, 2.2.2)
·
Find the distance between two complex
numbers. (2.2.2)
·
Find roots of complex numbers. (2.2.2,
e.g., #12, 13)
·
Prove properties of complex numbers. (e.g.,
2.2.1, #2; 2.2.2, #5)
·
Describe geometric
aspects of complex numbers (2.2.1,
2.2.2)
·
Know basic
information about contributions of historical mathematical personalities to the
development of the theories of real and complex numbers. (Information
in the introductions to Units 2.1 and 2.2)