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If z(1)=1+i sqrt(3) , z(2)=1-i sqrt(3), ...

If `z_(1)=1+i sqrt(3) , z_(2)=1-i sqrt(3),` then `(z_(1)^(100)+z_(2)^(100))/(z_(1)+z_(2))=`

A

a.`2^(100)`

B

b.`2^(-100)`

C

c.`-2^(100)`

D

d.`-2^(99)`

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The correct Answer is:
D
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. For any integer n, the argument of ((sqrt(3)+i)^(4 n+1))/((1-i sqrt(3)...

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  3. If z(1)=1+i sqrt(3) , z(2)=1-i sqrt(3), then (z(1)^(100)+z(2)^(100))/(...

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  4. If z(1)=1+i, z(2)=sqrt(3)+i, then arg ((z(1))/(z(2)))^(50)=

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  5. If 1,a(1), a(2). ..., a(n-1) are n roots of unity, then the value of (...

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  7. If |z(1)-1|lt2,|z(2)-2|lt1, then |z(1)+z(2)|

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  8. If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...

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  13. The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is rea...

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  16. If z(1), z(2) are two complex numbers such that Im(z(1)+z(2))=0 and Im...

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  17. If alpha is an imaginary fifth root of unity then log (2)|1+alpha+alph...

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  18. If |z+bar(z)|+|z-bar(z)|=8 then z lies on

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  20. If |z|=k and w=(z-k)/(z+k), then Re (w)=

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