It's hard to believe you are serious- or that whoever gave you those problems is serious. Both of these are very deep proofs. For the first one it is probably best to start by proving it for x and y positive integers and work your way up through the various number systems (integers, rational numbers, real numbers).

The second is a special case of the "fundamental theorem of algebra" but perhaps not as hard as I thought at first. Given any complex number a+ bi, write (x+ yi)^2= a+ bi. Multiply it out, equate real part to real part, and solve the two real number equations for x and y.