Hi,

first of all, Merry Christmas! I am doing some math while digesting another huge dinner, and have a small question.

Problem:

If A is any set of real numbers, define a function as follows:

Find expressions for and and

Attempt:

The way I am reading this, is that I first have to define a function which is 1 for real numbers, and 0 for pure imaginary numbers.

I think this one works fine:

where is the complex conjugate.

I am not so sure about the other expressions. If I still take B to be the set of pure imaginary numbers am I suppose to define the following functions:

Thank you for your time.