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On the Argand plane z1, z2a n dz3 are re...

On the Argand plane `z_1, z_2a n dz_3` are respectively, the vertices of an isosceles triangle `A B C` with `A C=B C` and equal angles are `thetadot` If `z_4` is the incenter of the triangle, then prove that `(z_2-z_1)(z_3-z_1)=(1+sectheta)(z_4-z_1)^2dot`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a^2+c^2=-a b ...

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  2. If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqr...

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  3. On the Argand plane z1, z2a n dz3 are respectively, the vertices of an...

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  4. If complex number z(z!=2) satisfies the equation z^2=4z+|z|^2+(16)/(|z...

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  5. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are ...

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  6. Find the locus of the points representing the complex number z for...

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  7. The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two ...

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  8. Identify the locus of z if bar z = bar a +(r^2)/(z-a).

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  9. If the expression (1 + ir)^3 is of the form of s(1+ i) for some real '...

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  10. Two towns A and B are 60 km a part. A school is to be built to serve ...

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  11. Find the amplitude of sinalpha+i(1-cosalpha)

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  12. Modulus of non zero complex number z satisfying barz +z=0 and |z|^2-4...

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  13. Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+...

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  14. Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary p...

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  15. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

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  16. Let f(x), g(x), and h(x) be the quadratic polynomials having positive ...

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  17. Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

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  18. If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where...

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  19. If a ,b ,c be the sides of A B C and equations a x^2+b x+c=0 and 5x^2...

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  20. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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