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If I m((z-1)/(e^(thetai))+(e^(thetai))/(...

If `I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0` , then find the locus of `z`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then fin...

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  2. If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of t...

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  3. If I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0 , then find the locus ...

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  4. If pa n dq are distinct prime numbers, then the number of distinct im...

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  5. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

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  6. What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-p...

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  7. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

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  8. The number of integral values of a for which the quadratic equation (x...

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  9. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

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  10. If z is a complex number having least absolute value and |z-2+2i|=1,th...

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  11. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, th...

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  12. Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/...

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  13. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

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  14. The number of the real solutions of the equation x^2-3absx+2=0 is

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  15. If |z-1| + |z + 3| le 8, then prove that z lies on the circle.

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  16. If z1a n dz2 are the complex roots of the equation (x-3)^3+1=0,t h e n...

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  17. If the quadratic equation a x^2+b x+6=0 does not have real roots and b...

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  18. If the equation |z-a|+|z-b|=3 represents an ellipse and a ,b in C ,w ...

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  19. If |z^2-3|=3|z| , then the maximum value of |z| is a.1 b. (3+sqrt...

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  20. What is the minimum height of any point on the curve y=x^2-4x+6 above ...

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