#((-1+i sqrt 3)/(-1-i))^2010#?

1 Answer
Cem Sentin
Mar 25, 2018

#-2^1005i#

Explanation:

#-1+isqrt3=2Cis120# and #-1-i=sqrt2*Cis225#

Hence,

#((-1+isqrt3)/(-1-i))^2010#

=#((2Cis120)/(sqrt2Cis225))^2010#

=#(2/sqrt2)^2010*(Cis(120-225))^2010#

=#(sqrt2)^2010*(Cis(-105))^2010#

=#2^1005*Cis((-105)*2010)#

=#2^1005*Cis(-211050)#

=#2^1005*Cis270#

=#-2^1005i#

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