Homework Assignment 4

Due : May 7, 2004. No extensions!

My "hunch" about the geometric series summation working for complex numbers "a" appears to be correct!

Write a Java program that will compute and print the sum of a geometric series

    S = a + a^2 + a^3 + ... + a^n

in three different ways: (1) Using a basic for-loop to walk along terms in the series, (2) Using Horner's method of multiplication, and (3) Using the geometric series summation formula. I believe that I have already given you all of the relevant details for method (2) and (3) in class.

The two files that you will need are Complex.java and GeometricSeries.java . The first file is a small library for creating and manipulating complex number objects. You shouldn't need to change this file. The second file is a skeleton solution ... with the key details removed.

You can solve this problem by simply filling in the missing details from GeometricSeries.java.

Here is a fragment of I/O from my solution:

prompt >> java GeometricSeries
Welcome to the Geometriic Series Computer
-----------------------------------------
Please enter complex number "a"
Coefficent a : Real : 1.0
Coefficent a : Imaginary : 2.0
Please enter number of terms in series "a" : 3

The complex no you have entered is :s = 1.0+2.0i
No of terms in series is = 3

Summation with basic for-loop        
======================================= 
Summation 1 = -13.0+4.0i

Summation using Horner's formula
======================================= 
Summation 2 = -13.0+4.0i

Summation with geometric-series formula 
======================================= 
Summation 3 = -13.0+4.0i

In this case, "a = 1 + 2i" and the series summation has 3 terms.
The corresponding hand calculation is as follows:

    S = a + a^2 + a^3 
      = (1 + 2i) + (1 + 2i)*(1 + 2i) + (1 + 2i)*(1 + 2i)*(1 + 2i)
      = (1 + 2i) + (1 + 4i - 4) + (1 + 4i - 4 + 2i - 8 - 8i)
      = -13 + 4i

Your solution to the three parts should be about 30-35 lines of Java, consisting of calls to appropriate methods in the Complex arithmetic library, and for-loop and if-else statements.

Note. Hand in a copy of your program source code and a script of I/O for typical program usage. To create a script, type something like:

    prompt >> script output-file

Now all input/output on the screen will be echoed to the file "output-file". To terminate the script, type:

    prompt >> exit

Now print "output-file" and hand it in.