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If z^2+z|z|+|z^2|=0, then the locus z is...

If `z^2+z|z|+|z^2|=0,` then the locus `z` is a. a circle b. a straight line c. a pair of straight line d. none of these

A

a circle

B

a straight line

C

a pair of straight lines

D

none of these

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The correct Answer is:
c
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. If z(1),z(2), z(3) are vertices of an equilateral triangle with z(0) i...

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  2. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

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  3. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

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  4. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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  5. Let g(x) and h(x) are two polynomials such that the polynomial P(x) =g...

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

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  7. If |z(1)|=|z(2)|=|z(3)| and z(1)+z(2)+z(3)=0, then z(1),z(2),z(3) are ...

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  8. If x(n)=cos(pi/3^(n))+isin((pi)/(3^(n))), then x(1),x(2),x(3),……………….....

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  9. If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, then (a1^2+b1^2)(a2^2+b2^2).......

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  10. If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)^(n) ...

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  11. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 then the ...

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  12. If alpha,beta,gamma are the cube roots of p, then for any x,y,z (x al...

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  13. Prove that t a n(i(log)e((a-i b)/(a+i b)))=(2a b)/(a^2-b^2)(w h e r ea...

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  14. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  15. The locus of the points representing the complex numbers z for which |...

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  16. For n=6k, k in z, ((1-isqrt(3))/(2))^(n)+((-1-isqrt(3))/(2))^(n) has t...

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  17. The product of all values of (cosalpha+isinalpha)^(3//5) is

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  18. If C^(2)+S^(2)=1, then (1+C+iS)/(1+C-iS) is equal to

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  19. The center of a square ABCD is at z=0. The affix of the vertex A is z(...

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  20. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

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