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The complex numbers z1, z2 and z3 satisf...

The complex numbers `z_1, z_2 and z_3` satisfying `(z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2` are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

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  2. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

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  3. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

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  4. Find the value of a for which the sum of the squares of the roots of t...

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  5. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

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  6. If x1, a n dx2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, ...

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  7. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cospi/4 (b) sinp...

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  8. If p ,q in {1,2,3,4,5} , then find the number of equations of form p^2...

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  9. If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+...

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  10. Find the domain and the range of f(x)=sqrt(x^2-3x.)

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  11. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

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  12. Find the domain and range of f(x)=sqrt(3-2x-x^2)

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  13. If x in (0,pi//2)a n dcosx=1//3 , then prove that sum(n=0)^oo(cosn x)/...

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  14. Prove that if the equation x^2+9y^2-4x+3=0 is satisfied for real value...

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  15. Let Zp=rp(costhetap+isinthetap),p=1,2,3a n d1/(Z1)+1/(Z2)+1/(Z3)=0. Co...

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  16. Find the least value of ((6x^2-22 x+21))/((5x^2-18x+17)) for real xdot

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  17. Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' ...

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  18. Find the range of the function f(x)=x^2-2x-4.

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  19. If x=9^(1/3) 9^(1/9) 9^(1/27) ...->∞ , y= 4^(1/3) 4^(-1/9) 4^(1/27) ....

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  20. Find the linear factors of 2x^2-y^2-x+x y+2y-1.

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