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If z1,z2,z3 be the vertices of an equila...

If `z_1,z_2,z_3 `be the vertices of an equilateral triangle, show that `1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)= 0 or z_1^2+z_2^2+z_3^2= z_1z_2+z_2z_3+z_3z_1`.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. The complex numbers z1, z2 and the origin form an equilateral triangle...

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

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

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

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

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  6. The points representing cube roots of unity

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

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

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

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

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

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  12. The equation zbarz+abarz+baraz+b=0, b in R represents circle, if

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  13. Prove that |z-z1|^2+|z-z2|^2 = k will represent a circle if |z1-z2|^2 ...

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  14. Find all circles which are orthogonal to |z|=1and|z-1|=4.

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  15. If z=4i-5 then |z| = and barz = .

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  16. If the conjugate of (x +iy) (1-2i) be 1+ i, then:

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  17. If |z|=2 and arg (z)=pi/4 , find zdot

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  18. In the Argand plane, the vector z = 4 - 3i is turned in the clockwise ...

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  19. The value of i^103 + i^(-99) = where i = sqrt(-1) .

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  20. The greatest and the least absolute value of z+1 where |z+4| le3 are ...

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