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Assignment 2 with 5 Questions - Complex Variables | MATH 355, Assignments of Mathematics

Christopher Newport University (CNU)Mathematics
Prof. P. P. Khalili

Material Type: Assignment; Professor: Khalili; Class: Complex Variables; Subject: Mathematics; University: Christopher Newport University; Term: Spring 2007;

Typology: Assignments

Pre 2010

Uploaded on 08/19/2009

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Department of Mathematics
Christopher Newport University
Math 355-01 Complex Variables Spring Term 2007
Homework # 2
Due Friday Jan.26.07
1. Simplify each expression.
(a) ๎˜2 + i
1 + 2i๎˜‘โˆ’๎˜i
2โˆ’i๎˜‘
(b) ๎˜Œ
๎˜Œ
๎˜Œ๎˜3 + i
1 + 2i๎˜‘3๎˜Œ
๎˜Œ
๎˜Œ
(c) (1 โˆ’iโˆš3 )5
2. Show that the hyperbola x y = 1 ,can be written z2
โˆ’z2= 4 i .
3. Find the principal argument Arg z , where
z=i
1โˆ’i
4. Find all of the roots in rectangular coordinates (โˆ’32)
1
5.
5. Find the four roots of the equation z4+1+i= 0 ,and give the absolute value of each root.

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Department of Mathematics

Christopher Newport University

Math 355-01 Complex Variables Spring Term 2007

Homework # 2

Due Friday Jan.26.

  1. Simplify each expression.

(a)

2 + i

1 + 2i

i

2 โˆ’ i

(b)

3 + i

1 + 2i

(c) (1 โˆ’ i

5

  1. Show that the hyperbola x y = 1 , can be written z 2 โˆ’ z

2 = 4 i.

  1. Find the principal argument Arg z , where

z =

i

1 โˆ’ i

  1. Find all of the roots in rectangular coordinates (โˆ’32)
  1. Find the four roots of the equation z

4

  • 1 + i = 0 , and give the absolute value of each root.