[math-fun] ridiculously simple derivation (whose?) of Pythagorean triples

In[570]:= (1+2*I)/(2+1*I) Out[570]= 4/5+(3 I)/5 In[571]:= (1+3*I)/(3+1*I) Out[571]= 3/5+(4 I)/5 In[572]:= (2+3*I)/(3+2*I) Out[572]= 12/13+(5 I)/13 In[573]:= (1+4*I)/(4+1*I) Out[573]= 8/17+(15 I)/17 In[586]:= Simplify/@ComplexExpand[(a+I*b)/(b+I*a)] Out[586]= (2 a b)/(a^2+b^2)-(I (a^2-b^2))/(a^2+b^2)