01-08-2016
Mathematics

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simplify 4/-2-2i please help

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dalendrk dalendrk

01-08-2016

[tex]\dfrac{4}{-2-2i}=\dfrac{4:(-2)}{(-2-2i):(-2)}=\dfrac{-2}{1+i}=-\dfrac{2}{1+i}\cdot\dfrac{1-i}{1-i}\\\\=-\dfrac{2(1-i)}{(1+i)(1-i)}=-\dfrac{2(1+i)}{1^2-i^2}=-\dfrac{2(1+i)}{1-(-1)}=-\dfrac{2(1+i)}{1+1}\\\\=-\dfrac{2(1+i)}{2}=-(1+i)=-1-i[/tex]

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