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What is the smallest positive integer n ...

What is the smallest positive integer `n` for which `(1+i)^(2n)=(1-i)^(2n)?`

A

4

B

8

C

2

D

12

Text Solution

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The correct Answer is:
C
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ML KHANNA-COMPLEX NUMBERS -Problem Set (3) (M.C.Q)
  1. ((1-i)/(1+i))^2=

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  2. The smallest positive integer n forwhich ((1 + i)/(1 - i))^(n) = 1 is:

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  3. What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n...

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  4. The smallest positive integral value of n for which ((1-i)/( 1+i))^(n)...

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  5. (2^(n))/( (1 - i)^(2 n)) + ((1 + i )^(2 n))/( 2^(n)) , n in I is equa...

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  6. If the number ((1 - i)^(n))/( (1 + i)^(n - 2)) is real and positive , ...

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  7. ((1 + i)^(2 n + 1))/( (1 - i) ^( 2 n - 1)), n in N in ( r, theta ) fo...

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  8. (1 + 7 i)/( (2 - i)^(2)) i n ( r , theta) form is

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  9. If ((1+i)/(1-i))^(3) - (( 1-i)/( 1+i))^(3) = x+iy , then (x,y) is equ...

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  10. The complex number(1+2i)/( 1-i) lies in the Quadrant number

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  11. i^(57) + 1// i^(125) , when simplified has the value

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  12. The value of 1+ i^(2) + i^(4) + i^(6)+"………"i^(2n) is

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  13. The value of i^2 + i^4 + i^6 + i^8....upto (2n+1) terms , where i^2 = ...

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  14. If i = sqrt(-1) and n is a positive integer, then i^(n) + i^(n + 1)...

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  15. One of the values of i^i is

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  16. If ( x + iy) ( 2 - 3 i) = 4 + i then

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  17. If ((1 + i) x- 2 i)/( 3 + i) + (( 2 - 3 i ) y + i)/( 3 - i) = i then...

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  18. If z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2), then lambda...

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  19. If z = x + iy, , x , y real and | x| + | y| le lambda | z| " then "...

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  20. If sqrt( x + iy) = pm (a + ib) , " then " sqrt( - x - iy) is equal to

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