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Complex number z1, z2 and z3 in AP...

Complex number `z_1, z_2 and z_3` in AP

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For any three complex numbers z_1, z_2 and z_3 , prove that z_1 lm (bar(z_2) z_3)+ z_2 lm (bar(z_3) z_1) + z_3lm(bar(z_1) z_2)=0 .

If the triangle fromed by complex numbers z_(1), z_(2) and z_(3) is equilateral then prove that (z_(2) + z_(3) -2z_(1))/(z_(3) - z_(2)) is purely imaginary number

Prove that traingle by complex numbers z_(1),z_(2) and z_(3) is equilateral if |z_(1)|=|z_(2)| = |z_(3)| and z_(1) + z_(2) + z_(3)=0

If the complex numbers z_1, z_2, z_3, z_4 taken in that order, represent the vertices of a rhombus, then

If the complex numbers z_(1),z_(2),z_(3) are in AP, then they lie on

Consider the complex numbers z_(1) and z_(2) Satisfying the relation |z_(1)+z_(2)|^(2)=|z_(1)| + |z_(2)|^(2) Complex number z_(1)//z_(2) is

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If |z-25i| lt= 15. then |"maximum " arg(z) - "minimum " arg(z)| equals

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  2. Find the complex number Z, the greatest in absolute value which satisf...

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  3. Complex number z1, z2 and z3 in AP

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  4. if |(1-iz)/(z-i)|=1 prove that the locus of the variable point z in th...

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  5. The equation barbz+bbarz=c, where b is a non-zero complex constant and...

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  6. Let A(z1) and (z2) represent two complex numbers on the complex plan...

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  7. Find the area of the triangle whose vertices in the Argand plane are i...

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

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  9. Find the area of the triangle whose vertices represent the three roots...

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  10. The complex numbers z1, z2 and the origin form an equilateral triangle...

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

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  12. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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  13. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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

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  15. The points representing cube roots of unity

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  16. z, w, w^2 are the vertices of an equilateral triangle in the Argand pl...

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  17. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

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  18. If two consecutive vertices of a regular hexagon be z and barz , find ...

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  19. If z1,z2 are two complex numbers representing two consecutive vertices...

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  20. If two vertices of an equilateral triangle are z1,z2 then find the com...

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