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

If n is of the form 3m+2, `1+omega^(-11) +omega^(-2n)` = _______ where `omega` is a nonreal cube root of 1.

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. The greatest and the least absolute value of z+1 where |z+4| le3 are ...

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

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

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

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

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  6. If omega is a cube root of unity, then find the value of the following...

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  7. Let the point P represent the complex number z. If OP is turned round ...

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  8. |sqrtz|^4 = where z is a unimodular complex number.

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  9. (z|barz|^2)/(barz|z|^2) = where z is a complex number of amplitude pi...

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  10. ABCD is a rhombus. Its diagonals AC and BD intersect at the point M a...

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  11. The angle that the vector representing the complex number 1/((sqrt3+i)...

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  12. If |z| =2 then then the complex number 1/z is represented on a fixed .

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  13. If z1 and z2 are two complex number and a, b, are two real number then...

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  14. a and b are real numbers between 0 and 1 such that the points z1 =a+ i...

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  15. If the complex number z1,z2 and z3 represent the vertices of an equila...

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  16. If the real part of (z+4)/(2z+i) is 1/2 then the point z lies on .

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  17. If a gt 0 ,b gt 0 then sqrt(-a) * sqrtb is equal to

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  18. If i^2=-1 then the value of sum(n=1)^200 i^n is

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  19. Find the smallest positive integer value of n for which ((1+i)^n)/((1-...

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  20. The digit in the units place in the value of (727)^39 is

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