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If `z_(1) ` and `z_(2)` are two complex numbers such that `|z_(1)| lt 1 lt |z_(2)|`, then prove that `|(1- z_(1)barz_(2))//(z_(1)-z_(3))| lt 1`

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The correct Answer is:
` rArr |(1 - z_(1) barz_(2))/(z_(1) - z_(2))| lt 1 `
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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
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  3. If z(1) and z(2) are two complex numbers such that |z(1)| lt 1 lt |z...

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  5. Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...

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  7. If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5, then (a)...

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  8. Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1)), where x and y are re...

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  9. Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) T...

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  10. If (x-alpha)/(z+alpha)(alpha in R) is a purely imaginery number and |z...

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  11. Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...

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  12. if z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) ), then ( 1 + ...

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  13. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

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  14. Let z in c be such that |z| lt . If omega = (5 + 3z)/(5(1 - z)), then ...

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  15. If z = ((1+i)^(2))/(alpha-i), alpha in R has magnitude sqrt((2)/(5)) ...

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  16. Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=p...

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  17. The equation |z-1|=|z+1|,i= sqrt(-1)represents =

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  18. if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

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  19. if z is a complex number belonging to the set S={z:|z-2+i|gesqrt(5)} a...

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  20. Let alpha and beta are roots of equation x^(2)-x-1=0 with alpha > bet...

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