Algebra Question

Question

Determine the truth values for the following statements. Please provide a clear motivation.

a) 2+(-1)⁵ is a real number

b) For all complex numbers z and w, (z-bar+w)-bar = w-bar +z

Answer 1

The answer to a is "true".(-1)⁵=-1 and 2-1=1 which is real!

b is also true and the way I usually work with these kind of problems is to convert to the form a+bi. If you do that, you will readily see that the statement is true.