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Log(e) ((1 + i)/(1- i))=...

`Log_(e) ((1 + i)/(1- i))= `

A

`(pi)/(2)`

B

`-i"" (pi)/(2)`

C

`i"" (pi)/(2)`

D

`- (pi)/(2)`

Text Solution

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The correct Answer is:
C
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Observe the following lists {:("List-I","List-II"),((A) 1-(1)/(2)+(1)/(3)-(1)/(4)+(1)/(5)+...oo,(1)(2)/(3)+ (1)/(2)log2),((B)(1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+...oo,(2)log_(e )2),((C )(1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))...oo,(3)-log_(e )((4)/(5))),((D)1+(1)/(3.3^(3))+(1)/(5.3^(5))+...oo,(4)log_(e )((5)/(4))),(,(5)-log_(e )(1-(1)/(n+1))):} The correct match for List - I from List -II is

AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If zbarz=4 then the locus of z is

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  2. Match the items of List - I with those of List-II

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  3. If z = x +iy and P represents z in the Argand plane and mod (2z-3) = 4...

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  4. If z = (lambda + 3) + isqrt( 5 - lambda^(2)) , then the locus of z is...

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  5. If z=(x+iy) and if the point P in the Argarand plane represent z, then...

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  6. If z1=1+2i,z2=2+3i,z3=3+4i, " then " z1,z2and z3 represents the vertic...

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  7. If z is a complex number with |z|ge 5 . Then the least value of |z +...

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  8. (1 + x)^(n) = p(0) + p(1) x + p(2) x^(2) + … + p(n) x^(n) , then p(0)...

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  9. The cube roots of unity when represented on the Argand diagram form th...

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  10. If a , b , c in R such that a + b + c= 0 and az(1) + bz(2) + cz(3) = ...

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  11. In the Argand plane the area in square units of the triangle formed by...

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  12. If the area of the triangle on the complex plane formed by the point z...

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  13. If |z-2/z|=2 then the greatest value of |z| is

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  14. If |z| ge 3 , then the least value of |z + (1)/(z)| is

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  15. The value of (i)^(i) is

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  16. Log(e) ((1 + i)/(1- i))=

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  17. The real and imaginary points of log (1 + isqrt3) are

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  18. Assertion (A) : If 3 + iy is a root of x^(2) + ax + b = 0 then a = -6 ...

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  19. If log((1)/(sqrt(3))){(|z|^(2)-|z|+1)/(2+|z|)}gt -2 , then z lies insi...

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  20. If omega is a complex cube root of unity , then for any n gt 1 unde...

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