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For all complex niumbers `z_1, z_2` satisfying `absz_1=12` and `abs(z_2-3-4i)=5`, the minimum value of `abs(z_1-z_2)` is

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The complex numbers z1,z2 and z3 satisfying (z1-z3)/(z2-z3)=(1-isqrt3)...

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  2. The value of a so that the sum of the squares of the roots of the equa...

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  3. For all complex niumbers z1, z2 satisfying absz1=12 and abs(z2-3-4i)=5...

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

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  5. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cos(pi/4) (b) s...

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

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

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

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

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

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

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

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

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

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

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  17. if x=9^(1/3)9^(1/9)9^(1/27)…..infty,y=4^(1/3)4^(1/9)4^(1/27)…..infty a...

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

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  19. If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a)-sqrt(|a|b) (b...

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  20. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

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