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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 circle

B

a straight line

C

a pair of straight lines

D

none of these

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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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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If arg (z-z1)/(z2-z1) = 0 for three distinct complex numbers z,z1,z2 ...

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  2. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

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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. If a r g((z-2)/(z+2))=pi/4 then the locus of z is

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  5. zbarz+abarz+baraz+b=0 where binR represents a real circle of nonzero r...

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  6. Find the value of sqrt(20+48i)

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  7. If i^p=i^q where i^2=-1 then p-q is divisible by 4.

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  8. If z=(2+3i)/(3+2i), then |z|=

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  9. Find the solutions to the equation (z+i)^2 = 16.

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  10. If z is a nonreal compex number and |z|=1 then z^2+1/z^2=2 .

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  11. State true or false: If z= (cos2theta+isin2theta)/(costheta+isintheta)...

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  12. If two nonzero complex numbers z1,z2 be such that z1+z2 is real then t...

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  13. For complex numbersz1=x1+iy1" and " z2=x2+iy2 we write z1 cap z2 if x1...

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  14. If z is a nonzero complex number then (bar(z^-1))=(barz)^-1 .

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  15. If the points P and Q represent the complex numbers z and iz then angl...

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  16. If z1ne-z2 and |z1+z2|=|1/z1 + 1/z2| then :

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  17. Find z, if |(z+1)/(z+i)|=1

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  18. If in the Argand plane z1,z2,z3 and z4 are four points such that |z1|=...

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  19. State true or false: If zne0 then argz+argbarz=0.

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  20. Let z1 and z2 be the roots of z^2+pz+q=0. Then the points represented ...

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