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The smallest positive integral value of ' n ' such that
`[(1+sin (pi)/(8)+i cos (pi)/(8))(1+sin (pi)/(8)-i cos (pi)/(8))]^(n)` is purely imaginary is

A

2

B

8

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
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  2. If P is the point in the Argand diagrma correspoinding to the complex ...

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  3. The smallest positive integral value of ' n ' such that [(1+sin (pi)...

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  4. The least positive integer n, for which ((1+i)^(n))/((1-i)^(n-2))is po...

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  5. If x+i y=(-1+i sqrt(3))^(2010), then x=

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  6. The value of |(1+i sqrt(3))/((1+(1)/(i+1))^(2))|=

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  7. If omega is an imaginary cube root of unity ,then the value of (1-omeg...

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  8. If P(x, y) denotes z=x+i y in Argand's plane and |(z-1)/(z+2 i)|=1, t...

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  9. The argument of the complex number sin((6pi)/(5))+i(1+cos.(6pi)/(5)) i...

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  10. The maximum value of n lt 101 such that 1+sum(k=1)^(n)i^(k)=0 is

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  11. The value of (-1+sqrt(3))^(62)+(-1-sqrt(-3))^(62) is

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  12. All complex number z which satisfy the equation |(z-6 i)/(z+6 i)|=1 li...

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  13. If z is a complex number with |z|=1 and z+(1)/(z)=x+iy, then xy=

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  15. ((-1+i sqrt(3))/(2))^(50)+((-1-i sqrt(3))/(2))^(50)=

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  18. If z(1)=sqrt(3)-i, z(2)=1+i sqrt(3), then amp(z(1)+z(2))=

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  19. If x(r)=cos. (pi)/(2^(r))+ isin. (pi)/(2^(r)), then x(1)x(2)x(3)....oo...

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  20. The product of the values of (cos ((pi)/(3))+i sin( (pi)/(3)))^(3 / 4)...

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