3.1-1 Let f(n) and g(n) be asymptotically nonnegative functions. Using the basic definition of O-notation, prove that max{f(n), g(n)}=O(f(n)+g(n)).

3.1-2 Show that for any real constants a and b, where b > 0, (n+a)^b= O(n^b).

3.1-4 Is 2^(n+1)=O(2^n)? Is 2^(2n)=O(2^n)?

4.2-7 Show how to multiply the complex numbers a+bi and c+di using only three multiplications of real numbers. The algorithm should take a, b, c, and d as input and produce the real component ac-bd and the imaginary component ad+bc separately.

* Write a pseudo code for A*B with complexity O(n^(log₃5)). (divide to 3 pieces)