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P is a point on the argand diagram on th...

P is a point on the argand diagram on the circle with OP as diameter two points Q and R are taken such that `angle POQ = angle QOR = theta`. If O is the origin and P, Q, R are are represented by complex `z_1, z_2, z_3` respectively then show that `z_2^2cos2 theta =z_1z_3 cos^2theta`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve the equation 12x^4-56 x^3+89 x^2-56 x+12=0.

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  2. If z is a complex number such that -pi//2lt=a r g zlt=pi//2, then whi...

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  3. P is a point on the argand diagram on the circle with OP as diameter t...

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  4. Solve the equation (x+2)(x+3)(x+8)(x+12)=4x^2

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  5. Given alpha,beta, respectively, the fifth and the fourth non-real root...

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  6. Solve the equation (x-1)^4+(x-5)^4=82.

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  7. If the six roots of x^6 = -64 are written in the form a + ib, where ...

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  8. The maximum area of the triangle formed by the complex coordinates z,...

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  9. Solve sqrt(x+5)+sqrt(x+21)=sqrt(6x+40.)

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  10. If zr : r=1,2,3, ,50 are the roots of the equation sum(r=0)^(50)z^r=0 ...

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  11. Evaluate the value of sqrt(6+sqrt(6+sqrt(6+…..to I nfi nity)))

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  12. If a complex number z satisfies |2z+10+10 i|lt=5sqrt(3)-5, then the le...

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  13. If 1,alpha1,alpha2, ,alpha(n-1) are the n t h roots of unity, prove t...

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  14. If n >1 , show that the roots of the equation z^n=(z+1)^n are collinea...

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  15. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  16. If |z2+i z1|=|z1|+|z2|a n d|z1|=3a n d|z2|=4, then the area of triang...

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  17. What is the locus of w if w=3/za n d|z-1|=1?

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  18. If z is complex number, then the locus of z satisfying the condition...

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  19. Find the remainder when x^3+4x^2-7x+6 is divided by x-1.

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  20. What is the locus of z if ||z-cos^(-1)cos12|-|z-sin^(-1)s in 12||=8(pi...

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