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Given z is a complex number with modulus...

Given `z` is a complex number with modulus 1. Then the equation `[(1+i a)/(1-i a)]^4=z` has all roots real and distinct two real and two imaginary three roots two imaginary one root real and three imaginary

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let r ,s ,a n dt be the roots of equation 8x^3+1001 x+2008=0. Then f...

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  2. Locate the region in the Argand plane determined by z^2+ z ^2+2|z^2|<...

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

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  4. The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1...

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  5. For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

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  6. The point z1=3+sqrt(3)i and z2=2sqrt(3)+6i are given on a complex plan...

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  7. The total number of integral values of a so that x^2-(a+1)x+a-1=0 has ...

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  8. If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

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  9. Let C1and C2 be two circles with C2 lying inside C1 A circle C lying i...

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  10. The number of positive integral solutions of x^4-y^4=3789108 is a.0 ...

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  11. The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior o...

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  12. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

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  13. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

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  14. If (log)(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in ...

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  15. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

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  16. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

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  17. If z=3/(2+costheta+"isin"theta) then locus of z is straight line a c...

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

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

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