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The complex numbers z1, z2 and the origi...

The complex numbers `z_1, z_2` and the origin form an equilateral triangle only if (A) `z_1^2+z_2^2-z_1z_2=0` (B) `z_1+z_2=z_1z_2` (C) `z_1^2-z_2^2=z_1z_2` (D) none of these

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Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

Prove that the complex numbers z_1 and z_2 and the origin form an isosceles triangle with vertical angle 2pi//3" if " z_1^2+z_2^2+z_1z_2=0

The complex numbers z_(1) and z_(2) and the origin form an isosceles trangle with vertical angle (2 pi)/(3), then a.z_(1)^(2)+z_(2)^(2)=z_(1)z_(2)bz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0c*z_(1)^(2)+z_(2)^(2)=3z_(1)z_(2)d none of these

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

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

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

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

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

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

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

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  8. The points representing cube roots of unity

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

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

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

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

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

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

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

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

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

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

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

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

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