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The z^2 + z|z| + |z|^2 = 0, then locus o...

The `z^2 + z|z| + |z|^2 = 0`, then locus of Z is

A

Circle

B

Straight line

C

A pair of straight lines

D

None of these

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
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  2. If arg z = pi/4 ,then

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  3. The z^2 + z|z| + |z|^2 = 0, then locus of Z is

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  4. The least value of p for which the two curves argz=pi/6 and |z-2sqrt(...

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  5. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  6. If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(...

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  7. The value of (x+omega+omega^(2)) (x +omega^(2)+omega^(4))(x +omega^(...

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  8. If z= (sqrt3-i)/2 , " then " (i^(101)+z^(101))^(103) erqual

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  9. The region of the complex plane for which |(z-a)/(z+veca)|=1,(Re(a) !=...

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  10. If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the loc...

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  11. In z is a complex number stisfying |2008z-1|= 2008|z-2|, then locus z ...

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  12. The locus of the points z satisfying the condition arg ((z-1)/(z+1))=p...

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  13. the locus of z=i+2exp(i(theta+pi/4)) is

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  14. If one vertex and centre of a square are z and origin then which of th...

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  15. if the complex no z1 , z2 and z3 represents the vertices of an equ...

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  16. If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

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  17. If z(1),z(2),z(3) and u,v,w are complex numbers represending the verti...

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  18. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

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  19. For two complex numbers z(1) and z(2) , we have |(z(1)-z(2))/(1-barz(1...

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  20. Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

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