What's wrong with my approach???

[monjinho]

With the problem 2/(1-i) * (1+i)/(1+i),

since (1+i)/(1+i) cancels out to a one, if you multiply one times 2/(1-i), don't you just get 2(1-i)??
For some reason, the answer is l+i.
Why can't you just make (1+i)/(1+i) equal one?

[stapel_eliz]

...if you multiply one times 2/(1-i), don't you just get 2(1-i)??

How are you getting that dividing by 1 - i is the same as multiplying by 1 - i?

Instead, try rationalizing the denominator. Don't cancel first; multiply out the denominator. What do you get?