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The roots of the equation 1+z+z^3+z^4=0 ...

The roots of the equation `1+z+z^3+z^4=0` are represented by the vertices of

A

equilateral triangle

B

square

C

rhombus

D

none

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The correct Answer is:
B
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ML KHANNA-COMPLEX NUMBERS -Problem Set (4) M.C.Q
  1. Let z(1) , z(2) be two non - zero complex numbers such that z(1)^(2)...

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  2. The origin and the roots of the equation z^2 + pz + q = 0 form an equi...

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  3. The roots of the equation 1+z+z^3+z^4=0 are represented by the vertice...

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  4. If the area of the triangle on the complex plane formed by the points ...

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  5. If the area of the triangle on the complex plane formed by complex num...

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  6. The area of the triangle (in square units) whose vertices are i, omega...

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  7. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

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  8. If z(1)=1+2i, z(2)=2+3i, z(3)=3+4i, then z(1),z(2) and z(3) represent ...

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  9. If |z(1)|=|z(2)|=|z(3)| and z(1)+z(2)+z(3)=0, then z(1),z(2),z(3) are ...

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  10. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  11. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  12. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

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  13. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

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  14. If z(1),z(2) are vertices of an equilateral triangle with z(0) its cen...

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  15. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

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  16. If a and b are real numbers between 0 and 1 such that the points z(1...

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  17. The centre of a square is at the origin and 1 + i is one of its verti...

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  18. The points 1 + i, 1 - i, - 1 + i and - 1 - i are

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  19. If one vertex of a square whose diagonals intersect at the origin is 3...

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  20. If z(1) and overline(z)(1) represent adjacent vertices of a regular po...

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