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If A=|z in C: z=x+ix-1 for all x in R} a...

If `A=|z in C: z=x+ix-1` for all `x in R}` and `|z| le |omega|` for all z, `omega in A`, then z is equal to

A

`1/2(1+i)`

B

`-1/2(1-i)`

C

`-1/2(1+i)`

D

`1/3(1-2i)`

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The correct Answer is:
b
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
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  2. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

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  4. If omega is a complex cube root of unity, then the equation |z- omega|...

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  5. If omega is a complex cube root of unity, then the equation |z- omega|...

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  8. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

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  9. If |z-4+3i| leq 1 and m and n be the least and greatest values of |z...

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  10. If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unit...

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  11. If z(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0...

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  12. The least positive integer n for which ((1+i)/(1-i))^n= 2/pi sin^-1 (...

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  14. If z(0)=(1-i)/2, then the value of the product (1+z(0))(1+z(0)^(2))(1+...

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  16. If the points in the complex plane satisfy the equations log(5)(|z|+3)...

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  17. A complex number z with (Im)(z)=4 and a positive integer n be such tha...

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  18. If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z(1)|...

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  19. If z(1) and z(2) satisfy the equation 2|z+3|=|"Re"(z)| and arg(z+3)/(1...

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  20. If A=|z in C: z=x+ix-1 for all x in R} and |z| le |omega| for all z, o...

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