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If z = x + iy lies in the third quadrant...

If z = x + iy lies in the third quadrant, then prove that `(barz)/(z)` also lies in the third quadrant when `y lt x lt 0`

A

`x gt y ge 0 `

B

`xlt y lt 0`

C

`y lt x lt 0 `

D

`y gt x gt 0 `

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VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
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  2. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

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  3. If z is a complex number such that |z|geq2 , then the minimum value...

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

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  5. Let z be a complex number such that the imaginary part of z is nonz...

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  6. Let z = x + iy be a complex number where x and y are integers. Then...

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  7. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  8. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  9. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

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  10. about to only mathematics

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  11. about to only mathematics

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

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

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  14. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  15. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  16. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  17. about to only mathematics

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  18. If z is complex number of unit modulus and argument theta then arg ...

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  19. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  20. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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  21. A man walks a distance of 3 units from the origin towards the North-...

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