SOLUTION: Simplify (1+2i)(1-2i).

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Question 529800: Simplify (1+2i)(1-2i).
Found 2 solutions by jim_thompson5910, nyc_function:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2B2i%29%2A%281-2i%29 Start with the given expression.


%281%29%281%29%2B%281%29%28-2i%29%2B%282i%29%281%29%2B%282i%29%28-2i%29 FOIL.


1-2i%2B2i-4i%5E2 Multiply.


1-2i%2B2i-4%28-1%29 Replace i%5E2 with -1. Note: i%5E2=-1.


1-2i%2B2i%2B4 Multiply.


5%2B0i Combine like terms.


5 Simplify


So %281%2B2i%29%2A%281-2i%29=5.


The expression is now in standard form a%2Bbi where a=5 and b=0


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Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
(1+2i)(1-2i) =
1 x 1 = 1
1 x -2i = -2i
2i x 1 = 2i
2i x (-2i) = -4(i^2)
1 - 2i + 2i -4(i^2)
1 - 4(-1) =
1 + 4 = 5

The answer is 5.