Find the product and write the result in standard form, a+bi

Question

(6+i)(6-i)=

I keep getting 37 but for some reason I feel like that's not the answer it wants!

Answer 1

It is 37!!!

(6+i)(6-i) = 36 + -6i + 6i - (-1) <-- FOIL

36 + -6i + 6i +1 <--- subtracting is the same as adding the opposite

= 36 + 1 <-- 6i cancels;

= 37

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checks by DIVISION!!!

37 37 (6+i)

----- = ----------------- <--- rationalizes the denomiantor

6-i (6-i)(6+i)

= 37(6+i)/37 <--- uses the same product we found above

= 6+i <-- same complex number we started with