A) \[x=-1,y=0\]
B) \[x=1,y=1\]
C) \[x=1,y=0\]
D) \[x=0,y=1\]
Correct Answer: C
Solution :
\[\sum\limits_{k=0}^{100}{{{i}^{k}}=x+iy,}\]Þ \[1+i+{{i}^{2}}\]\[+......+{{i}^{100}}=x+iy\] Given series is G.P. Þ \[\frac{1.(1-{{i}^{101}})}{1-i}=x+iy\] Þ \[\frac{1-i}{1-i}=x+iy\] Þ \[1+0i=x+iy\] Equating real and imaginary parts, we get the required result.You need to login to perform this action.
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