Finding the Sum of the square of two positive integers. 
Write the following equation as the sum of the square of two integers, $a^2 +b^2$.
  $$(8^2+5^2)(13^2+7^2)$$

I remember that you are supposed to do something with complex numbers or at least that is what my teacher did in class.

From identity $(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2$, that is easy to check, we get:
$$(8^2+5^2)(13^2+7^2)=(8\cdot13+5\cdot7)^2+(8\cdot7-5\cdot13)^2=139^2+9^2.$$
