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Consider the circle |z|=r in the Argand ...

Consider the circle `|z|=r` in the Argand plane, which is in fact the incircle of triangle `A B Cdot` If contact points opposite to the vertices `A ,B ,C` are `A_1(z_1),B(z_2)a n dC_1(z_3)` , obtain the complex numbers associated with the vertices `A ,B ,C` in terms of `z_1, z_2a n dz_3dot`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve the equation 3^(x^2-x)+4^(x^2-x)=25.

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  2. If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t...

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  3. Consider the circle |z|=r in the Argand plane, which is in fact the in...

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  4. Solve the equation 12x^4-56 x^3+89 x^2-56 x+12=0.

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

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  6. Locus of z if arg[z-(1+i)] = {:{(3pi//4 when |z| lt = |z-2|), (-pi//4 ...

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

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

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

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

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

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

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

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  14. The complex number associated with the vertices A, B, C of DeltaABC...

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  15. Evaluate x=sqrt(6+sqrt(6+sqrt(6+oodot)))

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

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

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

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

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  20. If |z2+i z1|=|z1|+|z2| and|z1|=3 and |z2|=4, then the area of triangl...

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