SOLUTION: I need to simplify this problem(5-2i)^2 I do not know if I did it right but the answer I got was 25-16i was I close?

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Question 173284: I need to simplify this problem(5-2i)^2 I do not know if I did it right but the answer I got was 25-16i was I close?
Found 4 solutions by jim_thompson5910, nerdybill, stanbon, monika_p:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285-2i%29%5E2 Start with the given expression.


%285-2i%29%2A%285-2i%29 Expand


%285%29%285%29%2B%285%29%28-2i%29%2B%28-2i%29%285%29%2B%28-2i%29%28-2i%29 FOIL.


25-10i-10i%2B4i%5E2 Multiply.


25-10i-10i%2B4%28-1%29 Replace i%5E2 with -1. Note: i%5E2=-1.


25-10i-10i-4 Multiply.


21-20i Combine like terms.


So %285-2i%29%5E2=21-20i.


So the expression is now in standard form a%2Bbi where a=21 and b=-20

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
%285-2i%29%5E2
%285-2i%29%285-2i%29
Applying FOIL:
25-10i-10i-4%29
25-20i-4%29
21-20i%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(5-2i)^2
Use Foil:
(5-2i)(5-2i)
F: 25
O: 5*-2i = -10i
I: 5*-2i = -10i
L: -2i*-2i = -4
--------------------
Combine to get:
21 - 20i
================
Cheers,
Stan H.

Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
remember that i^2=-1 then (-2i)^2=(-2)^2*i^2=4*(-1)=-4
(5-2i)^2=25-20i-4=21-20i