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The set of points z in the complex plane...

The set of points z in the complex plane satisfying `|z-i|z||=|z+i|z||` is contained or equal to the set of points z satisfying

A

`"lm"(z)=0`

B

`"Im"(z) le 1`

C

`|"Re"(z)| le 2`

D

`|z| le 3`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`|z-i|z||=|z+i|z||`
`|z/(|z|)-i|=|z/(|z|)+i|`
`rArr z/|z|` lies on real axis `rArr "Im"(z/|z|)=0 rArr "Im"(z)=0`
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  2. about to only mathematics

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  3. The set of points z in the complex plane satisfying |z-i|z||=|z+i|z|| ...

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  4. The set of points z satisfying |z+4|+|z-4|=10 is contained or equal to

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  5. If |omega|=2, then the set of points z=omega-1/omega is contained in o...

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  6. If |omega|=1, then the set of points z=omega+1/omega is contained in o...

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  7. The number of complex numbersd z, such that abs(z-1)=abs(z+1)=abs(z-i)...

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  8. Let alpha and beta be real and z be a complex number. If z^(2)+az+beta...

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  9. If omega=1 is the complex cube root of unity and matrix H=|{:(,omega,0...

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  10. The maximum value of |a r g(1/(1-z))|for|z|=1,z!=1 is given by.

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  11. about to only mathematics

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  12. Let a,b and c be three real numbers satisfying [a b c ] |(1,9,7),(...

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  13. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

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  14. about to only mathematics

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  15. If |z(1)|=|z(2)| and arg (z(1))+"arg"(z(2))=0, then

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  16. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

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  17. about to only mathematics

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  18. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  19. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  20. Let z(k)=cos(2kpi)/10+isin(2kpi)/10,k=1,2,………..,9. Then, 1/10{|1-z(1)|...

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