4. Pythagorean triples from complex in- tegers. A Gaussian integer is a complex number a + bi where both a and b are inte- gers. Let a, b be positive integers such that a > b. Let A+ Bi be the square of the Gaus- sian integer a + bi. a) Show that A, B and a2 + b2 form a Pythagorean triple. Just in case you have no idea what a complex number is, no prob- lem. The only thing you need to know is that (a + bi) 2 = a2 - 62 + 2abi and that therefore A = a2 -62 and B = 2ab. In other words, you are supposed to show that if a and b are positive integers, then (a2 - 62, 2ab, a2 + 62 ) is a Pythagorean triple. Still confused? Ask Burkard to clarify :) b) One of the Pythagorean triples on the an- cient Babylonian tablet Plimpton 322 that I showed you in one of the lectures is the crazy (4601, 4800, 6649). Can this particular triple be constructed in this way from a Gaussian integer? If this is possible, which Gaussian integer does the trick