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Material Type: Exam; Professor: Suslov; Class: Applied Complex Analysis; Subject: Mathematics; University: Arizona State University - Tempe; Term: Fall 2000;
Typology: Exams
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Instructor: S. K. Suslov
Name:
(1) (5 points each) Write the number in the form a + bi.
(a)
2 + 3i
1 − 2 i
1 − 2 i
2 + 3i
(b)
( 1 + i
1 − i
) 2 i^5
(c) (e i ) − 2 i
(d) e z , where z = 2e iπ/ 4
(2) (5 points) Describe the set of points z in the complex plane that satisfy |z| < 1 , Rez ≥ 0.
Date: September 20, 2000. 1
2 TEST 1, MAT 461
(3) (10 points) Find arg(1 −
3 i) and write 1 −
3 i in polar form. Find (1 −
3 i)^6.
(4) (5 points) Show that (
3 − i)^7 = − 64
3 + i64.
(5) (5 points) Sketch the set 0 < |z − i| < 1.
(6) (5 points each) Find the following limits:
(a) limz→ 2 i
z^2 + 4
z − 2 i
(b) limz→i
z 4 − 1
z^2 + 1
