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Simplify .\((1-2i)(1-i)(1+i)(1+2i)\)pls! fast!smiley

 Jul 10, 2018
 #1
avatar+21978 
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Simplify

(1-2i)(1-i)(1+i)(1+2i).

pls! fast!

 

\(\small{ \begin{array}{|rcll|} \hline && (1-2i)(1-i)(1+i)(1+2i) \\ &=& (1-2i)(1+2i)(1-i)(1+i) \quad | \quad (1-i)(1+i) = 1-i^2 \qquad (1-2i)(1+2i) = (1-(2i)^2) \\ &=& (1-(2i)^2)(1-i^2) \\ &=& (1-4i^2)(1-i^2) \quad | \quad i^2 = -1 \\ &=& (1-4(-1))(1-(-1)) \\ &=& (1+4)(1+1) \\ &=& (5)(2) \\ &=& 10 \\ \hline \end{array} }\)

 

laugh

 Jul 10, 2018

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