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

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MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - 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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  2. Without expanding the determinant at any stage, find K in R such that ...

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  3. Find the value of x and y which satisfy the following equations (x.y i...

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  4. Find x and y if: (i) (x+iy) + (7-5i)=9+4i

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  5. Given that x,yinR solve x^2-y^2-i(2x+y)=4i

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  6. Given that x,y in R, solve (2 + 3i) x^2 - (3-2i)y = 2x - 3y + 5i

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  7. Given that x,y in R : solve (4x^2+3xy)+(2xy-3x^2)iota=(4y^2-x^2/2)+(...

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  8. The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all ...

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  9. The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all ...

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  10. Let z be a complex number satisfying the equation z^3-(3+i)z+m+2i=0,w ...

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  11. If 2 and i are two roots of the equation 2z^4+az^3+bz^2+cz+3=0,where a...

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  12. The real values of the parameter 'a' for which at least one complex nu...

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  13. If |z1|=|z2|=dot=|zn|=1, prove that |z1+z2+z3++zn|=1/(z1)+1/(z2)+1/(z3...

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  14. If alpha & beta are any two complex numbers, prove that |alpha+beta|...

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  15. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

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  16. Prove the identity,|1-z1barz2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2)

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  17. Among the complex numbers z satisfying the condition |z+3-sqrt(3)i|=sq...

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  18. Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1), 'n' a positive integer ...

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  19. If alpha=e^(i2pi//7)a n df(x)=a0+sum(k-0)^(20)ak x^k , then prove that...

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  20. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

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