(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,

29=a^2 +b^2

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.