SOLUTION: Perform each of the indicated operation and express the result in the form a + in, where a, b € R 1. [Re[(5 + 3i) + (-1 + 2i)]]^2 2. [Im(1 + i)]^2

1.  You have this expression in the interior brackets 


        [(5 + 3i) + (-1 + 2i)].


    You should take the real part of it first.

    It is  5 + (-1) = 4.


    Then you should square it, and you get   = 16,  which is your  ANSWER.



2.  You have this expression in the interior parentheses 


        (1 + i).


    You should take the Imaginary part of it first.

    It is  the real number " 1 ", the coefficient at " i ",  according to the definition of an imaginary part 

        (see, for example, this Wikipedia article https://en.wikipedia.org/wiki/Complex_number )


    Then you should square it, and you get  1^2 = 1,  which is your   ANSWER.