How do you simplify #(3 + 4i) (3 + 4i)#?
Your first step would be just like if you multiplied together two binomials: factor out each to get a trinomial. If you use FOIL, it's easy: multiply the First terms, the Outer terms, the Inner terms, and the Last terms:
Sum these together, and you can get your halfway-simplified version:
We know that
Since standard imaginary form is