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Let alpha and beta be two fixed non-zero...

Let `alpha` and `beta` be two fixed non-zero complex numbers and 'z' a variable complex number. If the lines `alphabarz+baralphaz+1=0` and `betabarz+barbetaz-1=0` are mutually perpendicular, then

A

`alphabeta+bar(alpha)bar(beta)=0`

B

`alphabeta-bar(alpha)bar(beta)=0`

C

`bar(alpha)-alphabar(beta)=0`

D

`alphabar(beta)+bar(alpha)beta=0`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
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  2. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  3. Let alpha and beta be two fixed non-zero complex numbers and 'z' a var...

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  4. The center of a square is at z=0. A is z(1), then the centroid of the ...

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  5. If z=x+i y , then he equation |(2z-i)//(z+1)|=m represents a circle, t...

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  6. If x^2-2xcos theta+1=0, then the value of x^(2n)-2x^n cosntheta+1, n ...

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  7. If p^(2)-p+1=0, then the value of p^(3n) can be

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  8. If n in Z, then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

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  9. If arg (z(1)z(2))=0 and |z(1)|=|z(2)|=1, then

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  10. If omega is a complex cube root of unity, then ((1+i)^(2n)-(1-i)^(2n))...

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  11. If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n i...

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  12. x^(3m) + x^(3n-1) + x^(3r-2), where, m,n,r in N is divisible by

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  13. If z is nonreal root of [-1]^[1/7] then,find the value of z^86+z^175+z...

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  14. The locus of point z satisfying Re(z^(2))=0, is

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  15. The curve represented by "Im"(z^(2))=k, where k is a non-zero real num...

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  16. If log(tan30^@)[(2|z|^(2)+2|z|-3)/(|z|+1)] lt -2 then |z|=

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  17. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

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  18. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

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  19. If alpha,beta,gamma and delta are the equation x^(4)-1 = 0, then the v...

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  20. If omega is a complex cube root of unity, then the equation |z- omega|...

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