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If points A1, A2,…,A6 representing the c...

If points `A_1, A_2,…,A_6` representing the complex numbers `z_1, z_2,….,z_6` respectively the vertices of a regular hexagon and if `z_0` be the complex number representing centroid of the hexagon then prove that `z_(1)^(2) + z_(2)^(2) +….+z_(6)^(2)=6z_(0)^(2)`.

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FIITJEE-COMPLEX NUMBER-SOLVED PROBLEMS (SUBJECTIVE)
  1. Show that if iz^3+z^2-z+i=0, then |z|=1

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  2. Prove that, for integral value of n ge1, all the roots of the equation...

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  3. Find the complex number z satisfying the equations |(z-12)/(z-8i)|=5/...

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  4. If |z|ge3, then determine the least value of |z+(1)/(z)|.

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  5. ABCD is a rhombus. Its diagonals AC and BD intersect at the point M a...

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  6. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

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  7. Find z such that |z-2+2i|le 1 and |z| has (i) least absolute value ...

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  8. If points A1, A2,…,A6 representing the complex numbers z1, z2,….,z6 re...

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  9. z1,z2,z3 are complex number and p,q,r are real numbers such that: p/(|...

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  10. Show that the equation a z^3+b z^2+ b z+ a =0 has a root alpha such...

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  11. If 1/(a+omega)+1/(b+omega)+1/(c+omega)+1/(d+omega)=1/omega where a,b...

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  12. ABCD is a rhombus. Its diagonals AC and BD intersect at the point M a...

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  13. 1 1^(n+2)+1 2^(2n+1) is divisible by 133.

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  14. Using mathematical induction , show that (-(1)/(2^2))(1-(2)/(3^2))(1-(...

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  15. Show that H1 + H2 +…....+H(n) = (n+1)H(n) - n. where H(n) = 1 + (1)/(2...

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  16. cosx*cos2x*cos4x.....cos(2^(n-1)x)=(sin2^n x)/(2^nsinx)AAn in N

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  17. Show that 1+2x + 3x^2 +….+ nx^(n-1) = (1-(n+1)x^(n) + nx^(n+1))/((1-x)...

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  18. Find the sum tan^-1 x/ (1+1.2x^2)+tan^-1, x/(1+2.3x^2)+…+tan^-1, x/(1+...

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  19. Prove by mathematical induction that sum(r=0)^(n)r^(n)C(r)=n.2^(n-1), ...

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  20. Show that (d^n)/(dx^(n) )(x^(n) log x) = n! (log x + 1+(1)/(2) +…+(1)/...

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