Question 232815
Let's multiply a+bi and a-bi and see what happens:
{{{(a+bi)(a-bi) = a^2 -abi +abi -b^2i^2 = a^2 - b^2(-1) = a^2 + b^2}}}
The i's have disappeared. We're told that a and b are real numbers. Then {{{a^2 + b^2}}} is also a real number. Your answer is (2).