Show that for all n N.

To show:

Taking LHS,



[rationalize]



[ i2 = -1]


= (1 – i)n(1 + i)n


= [(1 – i)(1 + i)]n


= [(1)2 – (i)2]n [(a + b)(a – b) = a2 – b2]


= (1 – i2)n


= [1 – (-1)]n[ i2 = -1]


= (2)n


= 2n


= RHS


Hence Proved


1