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A, B, C are the point representing the complex numbers `z_1,z_2,z_3` respectively on the complex plane and the circumcentre of the triangle ABC lies at the origin. If the altitude of the triangle through the vertex A meets the circumcircel again at P, then prove that P represents the complex number `-(z_2z_3)/(z_1)`

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RESONANCE DPP-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z1=a+i b and z2=c+i d are two complex number such that |z1|=|z2|...

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  2. The centre of a square is at the point with complex number z0=1+i and...

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  3. Intercept made by the circle zbar z + alphabarz+baralpha z +r=0 on ...

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  4. The triangle formed by complex numbers z ,i z ,i^2z is (a)Equilatera...

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  5. If omega!=1 is n^(t h) root of unity, then value of sum(k=0)^(n-1)...

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  6. If product of the roots of the equation 3x^2-4x+(loga^2-log(-a)+3)=0 i...

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  7. The reflection of the complex number (2-i)/(3+i) , (where i=sqrt(-1) ...

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  8. If 0ltaltbltc and the roots alpha,beta of equation a="" x^2+b="" x+c="...

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  9. A, B, C are the point representing the complex numbers z1,z2,z3 respec...

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  10. ((-1+isqrt(3))/2)^6+((-1-isqrt(3))/2)^6+((-1+isqrt(3))/2)^5+((-1-isqrt...

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  11. The statement (a+i b)<(c+i d) is true for a^2+b^2=0 (b) b^2+d^2=0 ...

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  12. If alpha and beta are the roots of the equation x^2-x+1=0 , then alpha...

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  13. If alpha,beta,gamma are the cube roots of p(p<0), then for any x ,ya n...

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  14. If z1,z2,z3,z4 are imaginary 5th roots of unity, then the value of su...

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  15. If z and w are two complex number such that |z w|=1 and a rg(z)-a rg(...

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  16. Let z1,z2,z3 be non-zero complex numbers satisfying the equation z^4=i...

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  17. If z!=0 be a complex number and a rg(z)=pi/4, then R e(z)=I m(z)on l ...

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  18. The centre of a square ABCD is at z0dot If A is z1 , then the centroid...

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  19. The continued product of all values of (cosalpha+isinalpha)^(3/5) is 1...

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  20. The number of 15th roots of unity which are also the 25th root of u...

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