A) -1
B) 1
C) 0
D) 1
Correct Answer: A
Solution :
[a] we have, \[{{z}^{3}}+2{{z}^{2}}+2z+1=0\] \[\Rightarrow ({{z}^{3}}+1)+2z(z+1)=0\] \[\Rightarrow (z+1)({{z}^{2}}+z+1)=0\]\[\Rightarrow z=-1,\]\[\omega \],\[{{\omega }^{2}}\] Since z=-1 does not satisfy \[{{z}^{1985}}+{{z}^{100}}+1=0\]while z=\[\omega \],\[{{\omega }^{2}}\]satisfy it; hence, sum is \[\omega +{{\omega }^{2}}=-1\].You need to login to perform this action.
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