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If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3...

If `z_r=cos(pi/(3_r))+isin(pi/(3_r)),r=1,2,3, ,` prove that `z_1z_2z_3 z_oo=idot`

A

1

B

`-i`

C

`i`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-COMPLEX NUMBERS -Problem Set (2) (M.C.Q)
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  2. If z(r) = cos ( pi // 2^(r)) + i sin ( pi // 2 ^(r)) r = 1, 2, . . . ...

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  3. If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3, , prove that z1z2z3 zoo=idot

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  4. If z=ilog(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

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  5. The value of (tan(i*log((a-ib)/(a+ib)))) is

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  6. If x satisfies the equation x^(2) - 2 x cos theta + 1 = 0 then the ...

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  7. If 2 cos theta = x + (1)/( x) , 2 cos phi = y + (1)/( y) then

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  8. The equation whose roots are nth power of the roots of the equations...

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  9. If x^(2) - 2 x cos theta + 1 = 0 " then " x^(2 n) - 2 x ^(n) cos n th...

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  12. If a = cos alpha + i sin alpha , b = cos beta + i sin beta , " then ...

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  13. If cos A + cos B + cos C = 0, sin A + sin B + sin C = 0 and A + B +...

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  14. If cos A + cos B + cos C = 0 = sin A + sin B + sin C , then

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  15. The general value of x which satisfies the equation ( cos x + i sin ...

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  16. Find the theta such that (3+2i sin theta)/(1-2 isin theta) is (a) re...

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  17. If ( tan theta - i [ sin ( theta // 2) + cos ( theta // 2) ])/( 1 + 2...

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  19. The continued product of the four values of [ cos (pi/ 3) + i sin (...

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