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If `z_1, z_2 and z_3`, are the vertices of an equilateral triangle ABC such that ` |z_1 -i| = |z_2 -i| = |z_3 -i|`.then `|z_1 +z_2+ z_3| `equals:

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one re...

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  2. If z is any complex number such that |z+4|lt=3, then find the greatest...

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  3. If z1, z2 and z3, are the vertices of an equilateral triangle ABC suc...

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  4. If two roots of x^3-a x^2+b x-c=0 are equal in magnitude but opposite ...

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  5. For any complex number z find the minimum value of |z|+|z-2i|

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  6. The greatest positive argument of complex number satisfying |z-4|=R e(...

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  7. If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equat...

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  8. Prove that the distance of the roots of the equation |sintheta1|z^3+|s...

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  9. Let z1a n dz2 be two distinct complex numbers and let z=(1-t)z1+t z2 f...

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  10. If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then ...

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  11. If |z1-1|lt=1,|z2-2|lt=2,|z(3)-3|lt=3, then find the greatest value o...

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  12. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

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  13. If the roots of equation x^3+a x^2+b=0a r ealpha1,alpha2 and alpha3(a ...

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  14. If z is a complex number, then find the minimum value of |z|+|z-1|+|2z...

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  15. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

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  16. If alpha,betaa n dgamma are roots of 2x^3+x^2-7=0 , then find the va...

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  17. if z is complex no satisfies the condition | Z |>3. T...

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  18. If alpha is the nth root of unity, then 1+2alpha+3alpha^2+ ton terms e...

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  19. Let r ,s ,a n dt be the roots of equation 8x^3+1001 x+2008=0. Then f...

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  20. Locate the region in the Argand plane determined by z^2+ z ^2+2|z^2|<...

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