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Find the minimum value of the expression `E= |z|^2+ |z-3|^2 + |z- 6i|^2` (where `z=x+iy, x,y in R`)

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z +2 - i|=5 then the maximum value of |3z+9-7i| is K, then find k

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  2. If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in ...

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  3. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

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  4. The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and a...

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  5. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

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  6. Express 1/(1-costheta+2isintheta) in the form x+i y .

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  7. a ,b ,c are three complex numbers on the unit circle |z|=1, such that ...

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  8. If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the eq...

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  9. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

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  10. If |z1|=15 and |z2-3-4i|=5,t h e n

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  11. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

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  12. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

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  13. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

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  14. If alpha,beta are the roots of the equation a x^2+b x+c=0, then find t...

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  15. If (3pi)/2 < alpha < 2pi then the modulus argument of (1+cos 2alpha)+i...

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  16. The value of z satisfying the equation logz+logz^2+dot+logz^n=0 i s ...

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  17. If the difference between the roots of the equation x^2+a x+1=0 is les...

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  18. find the differtiation of (i) tan(secx) (ii) sin(tanx)

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  19. Roots of the equation are (z+1)^5=(z-1)^5 are (a) +-itan(pi/5),+-ita...

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  20. Find the value of a for which one root of the quadratic equation (a^2-...

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