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If z1^2+z2^2-2z1.z2.costheta= 0 prove t...

If `z_1^2+z_2^2-2z_1.z_2.costheta= 0 ` prove that the points represented by `z_1, z_2`, and the origin form an isosceles triangle.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta,gamma,delta are four complex numbers such that gamma/del...

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  2. If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilonR, th...

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  3. If z1^2+z2^2-2z1.z2.costheta= 0 prove that the points represented by ...

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  4. Prove that the circles z bar z +z( bar a 1)+bar z( a1 )+b1=0 ,b1 in ...

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  5. If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0...

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  6. If z0 is the circumcenter of an equilateral triangle with vertices z1,...

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  7. Two different non-parallel lines cut the circle |z| = r at points a...

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  8. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

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  9. Prove that |z-z(1)|^(2) + |z - z(2)|^(2) = a will represent a real ci...

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  10. Complex numbers z1 , z2 , z3 are the vertices A, B, C respectively of ...

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  11. Given that alpha , gamma are roots of the equation Ax^(2) - 4x + 1 ...

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  12. Show that the area of the triangle on the Argand diagram formed by the...

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  13. Intercept made by the circle zbar z +bar a+abar z+r=0 on the real a...

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  14. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

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  15. Show that if iz^3+z^2-z+i=0, then |z|=1

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  16. Show that the equation of a circle passing through the origin and ha...

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  17. The function f(x)=a x^2+b x^2+c x+d has three positive roots. If the ...

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  18. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

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  19. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

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  20. If (18 x^2+12 x+4)^n=a0+a(1x)+a2x2++a(2n)x^(2n), prove that ar=2^n3^r(...

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