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If |z-1| + |z + 3| le 8, then prove that...

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

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. omega is an imaginary root of unity. Prove that (a+bomega+comega^2)^3+...

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  2. The number of real solutions of |x|+2sqrt(5-4x-x^2)=16 is/are a. 6 ...

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

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

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

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

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

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

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  9. Find the locus of point z if z , i ,and iz , are collinear.

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  10. If |z-1|lt=2a n d|omegaz-1-omega^2|=a where omega is cube root of unit...

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  11. What is the maximum height of any point on the curve y=-x^2+6x-5 above...

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  12. Consider an ellipse having its foci at A(z1)a n dB(z2) in the Argand p...

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  13. The roots of the cubic equation (z+ ab)^(3) = a^(3), such that a ne 0...

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  14. Find the largest natural number a for which the maximum value of f(x)=...

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  15. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

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  16. If omega is a complex nth root of unity, then sum(r=1)^n(ar+b)omega^(r...

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  17. Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3...

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  18. If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+2) , then prove that z1, z2, z3...

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  19. If |z1/z2|=1 and arg (z1z2)=0 , then a. z1 = z2 b. |z2|^2 = z1*z2 ...

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  20. Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h ...

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