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The roots of the cubic equation (z + alp...

The roots of the cubic equation (z + `alpha` `beta`)^3 = `alpha`^3 , `alpha` is not equal to 0, represent the vertices of a triangle of sides of length

A

`1/sqrt(3)|alphabeta|`

B

`sqrt(3)|alpha|`

C

`sqrt(3)|beta|`

D

`1/sqrt(3)|alpha|`

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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The curve represented by "Im"(z^(2))=k, where k is a non-zero real num...

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

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

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

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

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

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

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  8. The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radiu...

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  9. z is such that a r g ((z-3sqrt(3))/(z+3sqrt(3)))=pi/3 then locus z is

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  10. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

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  11. If |z-4+3i| leq 1 and m and n be the least and greatest values of |z...

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  12. If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unit...

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  13. If z(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0...

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  14. The least positive integer n for which ((1+i)/(1-i))^n= 2/pi sin^-1 (...

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  15. The area of the triangle formed by the points representing -z,iz and z...

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  16. If z(0)=(1-i)/2, then the value of the product (1+z(0))(1+z(0)^(2))(1+...

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  17. The greatest positive argument of complex number satisfying |z-4|=R e(...

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  18. If the points in the complex plane satisfy the equations log(5)(|z|+3)...

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  19. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

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  20. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

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