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sab562 sab562
  • 31-07-2016
  • Mathematics
Answered

simplify 4/-2-2i please help

Verified Answer :

dalendrk
dalendrk dalendrk
  • 31-07-2016

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

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