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Show that the product [1+(1+i)/2][1+((1+...

Show that the product `[1+(1+i)/2][1+((1+i)/2)^2][1+((1+i)/2)^(2^2)]...[1+((1+i)/2)^(2^n)]` is equal to `(1-1/2^(2^n))(1+i)`

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The correct Answer is:
`(1-1/(2^(n)))(1+i)`
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MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Show that the product [1+(1+i)/2][1+((1+i)/2)^2][1+((1+i)/2)^(2^2)]......

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  3. A man walks a distance of 3 units from the origin towards the North...

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  4. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  5. A particle P starts from the point z(0)=1+2i, where i=sqrt(-1). It mov...

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  6. Let A ,B ,C be three sets of complex number as defined below A={z : I ...

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  7. Let A,B,C be three sets of complex number as defined below A={z:lm ...

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  8. Let A,B,C be three sets of complex number as defined below A={z:lm ...

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  9. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

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  10. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1)) ...

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  11. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  12. Let omega be a complex cube root unity with omega!=1. A fair die is th...

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  13. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

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  14. Let omega be the complex number " cos " ( 2pi)/(3) + isin (2pi)/(3)...

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  15. Match the statement in Column I with those in Column II. [Note : He...

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  16. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

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  17. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

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  18. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

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  19. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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  20. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  21. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

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