`((1+i)^2011)/(1-i)^2009`=

((1+i)/(1-i))^4+((1-i)/(1+i))^4=

For all real numbers x,let f(x)=(1)/(2011sqrt(1-x^(2011))) Evaluate (f(f...f(2011)))^(2011), where fis applied 2010 xx 2010 xx

1+(1+i)+(1+i)^(2)+(1+i)^(3)=

4+5((-1+i sqrt3)/2)^2008 +3((-1+i sqrt3)/2)^2009 =

if x+(1)/(x)=1 then x^(2009)+(1)/(x^(2009))

Given that, z=(1+2i)/(1-i)=((1+2i)(1+i))/((1-i)(1+i))