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The locus of the points z satisfying the...

The locus of the points z satisfying the condition arg `((z-1)/(z+1))=pi/3` is, a

A

A straight line

B

Circle

C

A parabola

D

Ellipse

Text Solution

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The correct Answer is:
B
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For a non-zero complex number z , let arg(z) denote the principal argument with pi lt arg(z)leq pi Then, which of the following statement(s) is (are) FALSE? arg(-1,-i)=pi/4, where i=sqrt(-1) (b) The function f: R->(-pi, pi], defined by f(t)=arg(-1+it) for all t in R , is continuous at all points of RR , where i=sqrt(-1) (c) For any two non-zero complex numbers z_1 and z_2 , arg((z_1)/(z_2))-arg(z_1)+arg(z_2) is an integer multiple of 2pi (d) For any three given distinct complex numbers z_1 , z_2 and z_3 , the locus of the point z satisfying the condition arg(((z-z_1)(z_2-z_3))/((z-z_3)(z_2-z_1)))=pi , lies on a straight line

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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the loc...

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

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

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

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

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

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

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

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

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

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

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  12. If the ratio of the roots of the equation lx^2+nx+n=0 is p:q prove tha...

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  13. For the equation |x^(2)| + |x| -6=0, the roots are

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  14. If a+b+c=0 and a,b,c are ratiional. Prove that the roots of the equati...

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  15. If secalpha, tanalpha are roots of ax^2 + bx + c = 0, then

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  16. If x is real then the values of (x^(2) + 34 x - 71)/(x^(2) + 2x - 7) d...

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  17. if alpha&betaare the roots of the quadratic equation ax^2 + bx + c = 0...

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  18. let alpha ,beta be roots of ax^2+bx+c=0 and gamma,delta be the roots o...

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  19. The equation (a(x-b)(x-c))/((a-b)(a-c)) + (b(x-c)(x-a))/((b-c)(b-a))+...

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  20. If z1=3−2i,z2=2−i and z3=2+5i then find z1+z2−3z3

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