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A,B and C are the points respectively th...

A,B and C are the points respectively the complex numbers `z_(1),z_(2)` and `z_(3)` respectivley, on the complex plane and the circumcentre of `/_\ABC` lies at the origin. If the altitude of the triangle through the vertex. A meets the circumcircle again at P, prove that P represents the complex number `(-(z_(2)z_(3))/(z_(1)))`.

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RESONANCE DPP ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. If z1=a+ib and z2=c+id are two complex numbers where a,b,c,d in R and...

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

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  4. Intercept made by the circle z z +a+a z+r=0 on the real axis on comp...

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  5. The triangle formed by the complex numbers z, iz , i^2z is :

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  6. The omega!= 1 is nth root unity, then value of sum(k=0)^(n-1)|z1+omega...

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

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

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

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  10. A,B and C are the points respectively the complex numbers z(1),z(2) an...

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  11. ((-1+isqrt(3))/2)^6+((-1-isqrt(3))/2)^6+((-1+isqrt(3))/2)^5+((-1-isqrt...

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

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  14. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

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

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

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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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