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The real and imaginary parts of log (1 +...

The real and imaginary parts of log `(1 + i)` =

A

`((1)/(2) , (pi)/(4))`

B

`(log 2 , (pi)/(4))`

C

`( log sqrt2 , (pi)/(4))`

D

`( log ""(1)/(2) , (pi)/(4))`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. Log (log i) =

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  2. The value of i^(i^(-i…..oo)) = x + iy then x^(2) + y^(2) =

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  3. The real and imaginary parts of log (1 + i) =

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  4. (sin (log i^(i)))^3 + (cos (log i^(i)))^3 =

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  5. z = 6. e^(i (pi)/(3)) then |e^(iz)| =

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  6. tan{ilog((a-ib)/(a+ib))}=

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  7. The locus represented by |z-1|=|z+i| is

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  8. Let z = 1 - t + isqrt(t^(2) + t + 2) , where t is a real parameter . T...

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  9. In the Argand Diagram , all the complex numbers z satisfying |z - 4i| ...

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  10. The region of the argand plane defined by |z-i| + |z +i| le 4 is

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  11. If (z+2)/(z+6i) is purely real then the locus of z = x +iy is

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  12. If |z -1| lt 2 |z - 2| then the locus of z = x + iy is

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  13. If the imaginary part of (2z + 1)/(iz+ 1) is -2 , then the locus of th...

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  14. z = x + iy and w = (1 - iz)/(z-i) , then |w| = 1 implies in the comple...

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  15. If Amp ((z+2)/(z-4i))=pi/2 then the locus of z = x + iy is .

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  16. If Arg ((2 - z)/(2 + z)) = (pi)/(6) and z = x + iy , then the locus of...

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  17. If omega=z/(z-1/3i) and |omega|=1 then z lies on

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  18. The points in the set {zinC: Arg " ((z-2)/(Z-6i))=pi/2} lie on the cu...

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  19. Statement - I : If n = 4m + 3 , is integer then i^(n) is equal to -i ...

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  20. The complex equation |z + 1- i| = |z + i-1| represents a

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