(a) It is an interesting fact that if
p is a prime number such that p -1 is
divisible by 4, then p can be written as the sum of two squares. (By a square,
we mean the square of an integer.) Find a complex number z whose real and
imaginary parts are both integers and such that zz(this z has a bar above it) = 29.
I know zz(bar)= a^2 + b^2 so,
but i dont know where to go from there
(b) Find four complex numbers z with the property that Re(z), Im(z),
Re(z-1) and Im(z-1) are all integers, where Re and Im denote the real and
imaginary parts respectively of a complex number.