h2> Programming Assignment 3 </h2>
<p>
Prob 1. Consider complex numbers a+ib where <MATH> i<sup>2</sup> = -1 </MATH>
and
a and b are reals. You may use float or double for reals !
                                                                                
Given two n-tuples p=(p1,p2,...,pn) and q=(qi,q2,...,qn) of complex
numbers, the inner product of p and
q, written < p|q > is the sum of pi* times qi, summed over all i from 1 thru
n. (Here, pi* is the complex conjugate a-ib of pi = a+ib). Compute
< p|q > and < q|p > and see how they are related.
<p>
Prob 2. To compute the exponentiation function power(x, t) where t is a
positive integer, we can use the following method. If t is even then
power(x,t) = power(x,t/2)*power(x, t/2). If t is odd then power(x,t) =
power(x, t-1)*x. Define the appropriate base cases and write a 
function based program to implement this strategy.  

<p>
Prob 3
 Verify that 
<pre>
             Fib(i+1) =   1  1 Fib(i)
             Fib(i)       1  0 Fib(i-1)
</pre>
  where Fib(i) is the i-th Fibonacci number. Use this relation to compute
Fib(n) for a given n. Can you  extend the method described in the 
previous problem ?