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`a` and `b` are real numbers between 0 and 1 such that the points `z_1 =a+ i`, `z_2=1+ bi`, `z3= 0` form an equilateral triangle, then `a` and `b` are equal to

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A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If |z| =2 then then the complex number 1/z is represented on a fixed .

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

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

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

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

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

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

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

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

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  10. If n is an integer, not a multiple of 3, the sum of w^n+w^(2n),w bein...

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  11. If alpha=root(3)(1) and alpha is not real then alpha^(3n+1)+alpha^(3n+...

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  12. If 1,omega,omega^(2) are the cube roots of unity, then the roots of t...

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  13. If z is a complex number then

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  14. If z=ibarz then

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  15. The value of sqrti is

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  16. Prove that (sqrt(3)/(2) +(i)/(2))^(5) + (sqrt(3)/(2) -(i)/(2))^(5) is...

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  17. If zr = sinfrac(2pir)(11)-icosfrac(2rpi)(11) then : the value of sum(r...

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  18. If zr = sinfrac(2pir)(11)-icosfrac(2rpi)(11) then : the value of sum(r...

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  19. The complex numbers sin x - i cos 2x and cos x - i sin 2x are conjugat...

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  20. If |z1|= |z2|=1 and amp z1+ampz2=0 then

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