SOLUTION: calculate and write in standard form: (1-2i)^2, I have worked it down to 4i^2-4i+1 but can't figure out how to work it down even more.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: calculate and write in standard form: (1-2i)^2, I have worked it down to 4i^2-4i+1 but can't figure out how to work it down even more.      Log On


   

Question 317789: calculate and write in standard form: (1-2i)^2, I have worked it down to 4i^2-4i+1 but can't figure out how to work it down even more.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281-2i%29%5E2 Start with the given expression.


%281-2i%29%281-2i%29 Expand


%281%29%281%29%2B%281%29%28-2i%29%2B%28-2i%29%281%29%2B%28-2i%29%28-2i%29 FOIL.


1-2i-2i%2B4i%5E2 Multiply.


1-2i-2i%2B4%28-1%29 Replace i%5E2 with -1. Note: i%5E2=-1.


1-2i-2i-4 Multiply.


-3-4i Combine like terms.


So %281-2i%29%5E2=-3-4i.