1)if z is any complex number, prove by induction that z^n/(z^n), can be expressed as a polynomial of degree n in the quantity w= z+ 1/z

2)(a^2+b^2)(c^2+d^2)=(ac-bd)^2 +(ad+bc)^2 prove by induction that r=a1,a2,a3...an where the a's represent the sums of 2 squares. it itself is a sum of two squares. Check it with: 2=1^2+1^2, 5=1^2+2^2, 8=2^2+2^2, for r=160, r=1600, r=1300, r=625

3) show that for 2 positive rational numbers, r=a/b and s= c/d r>s is equivalent to ac-bd>0

Thanks