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The points representing cube roots of un...

The points representing cube roots of unity

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Value and physical representation of Cube roots of Unity

Which one of the following is correct in respect of the cube roots of unity?

The sum and product of cube roots of unity is 0 and 1.

Find the equation of the circle in argand plane which passes through non real cube roots of unity and touches two sides of triangle with vertices as cube roots of unity

The value of |sqrtalpha| , where alpha is a nonreal cube root of unity , is _______.

If omega is an imaginary cube roots of unity such that (2+omega)^2=a+bomega,a,b in R then value of a+b is

If A is unimodular,then which of the following is unimodular? -A b.A^(-1) c.adjA d.omega A where omega is cube root of unity

Introduction and Cube root of Unity

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If z1,z2,z3 be the vertices of an equilateral triangle, show that 1/(z...

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

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  3. The points representing cube roots of unity

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If a+ib = x-iy then in terms of x,y we have a-ib = .

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  19. If n is of the form 3m+2, 1+omega^(-11) +omega^(-2n) = where omega is...

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  20. If alpha,beta,gamma are the cube roots of p then for any x,y and z (xa...

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