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Let a be a complex number such that |a|<...

Let `a` be a complex number such that `|a|<1a n dz_1, z_2,z_3,... ` be the vertices of a polygon such that `z_k=1+a+a^2+...+a^(k-1)` for all `k=1,2,3, T h e nz_1, z_2` lie within the circle (a)`|z-1/(1-a)|=1/(|a-1|)` (b) `|z+1/(a+1)|=1/(|a+1|)` (c) `|z-1/(1-a)|=|a-1|` (d) `|z+1/(a+1)|=|a+1|`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the square root 9+40 idot

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  2. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic e...

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  3. Let a be a complex number such that |a|<1a n dz1, z2,z3,... be the ve...

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  4. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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  5. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

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  6. Let z=1-t+isqrt(t^2+t+2), where t is real parameter. The locus of z in...

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  7. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

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  8. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

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  9. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

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  10. z^2+zabsz+absz^2=0 then the locus of z is

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  11. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

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  12. Solve the equation x^2+p x+45=0. it is given that the squared differen...

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  13. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

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  14. z1a n dz2 lie on a circle with center at the origin. The point of inte...

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  15. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

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  16. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

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  17. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

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  18. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

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  19. Find a quadratic equation whose product of roots x1 and x2 is equa...

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  20. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

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