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If z(1) and z(2) are two complex numbers...

If `z_(1)` and `z_(2)` are two complex numbers such that `|(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1`, then which one of the following is true?

A

`|z_(1)|=1, |z_(2)|=1`

B

`z_(1)=e^(itheta), theta in R`

C

`z_(2)=e^(itheta), theta in R`

D

all of these

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The correct Answer is:
b
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
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  2. Common roots of the equation z^(3)+2z^(2)+2z+1=0 and z^(2020)+z^(2018)...

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  3. If z(1) and z(2) are two complex numbers such that |(z(1)-z(2))/(1-bar...

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  4. The points representing cube roots of unity

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  5. If z(1) and z(2) are two complex numbers such that |(z(1)-z(2))/(z(1)+...

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  6. If z(1), z(2) are two complex numbers such that |(z(1)-z(2))/(z(1)+z(2...

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  7. If n is a positive integer greater than unity z is a complex number sa...

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  8. If n is a positive integer greater than unity z is a complex number sa...

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  9. If at least one value of the complex number z=x+iy satisfies the condi...

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  10. Given z is a complex number with modulus 1. Then the equation [(1+i a)...

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  11. The center of a regular polygon of n sides is located at the point z=0...

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  12. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

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  13. For any complex number z, the minimum value of |z|+|z-1|

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  14. The inequality |z-4| < |z-2| represents

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  15. Number of non-zero integral solution of the equation |1-i| ^(n)=2^(n),...

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  16. If "Im"(2z+1)/(iz+1)=-2, then locus of z, is

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  17. lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imagina...

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  18. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

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  19. If z(1),z(2), z(3) are vertices of an equilateral triangle with z(0) i...

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

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