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If x(n) + iy(n) = (1 + i)^(n) then x(n -...

If `x_(n) + iy_(n) = (1 + i)^(n)` then `x_(n - 1) y_(n) - x_(n) y_(n- 1)` =

A

`2^(n-2)`

B

`2^(n + 1)`

C

`2^(2n - 1)`

D

`2^(n-1)`

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The correct Answer is:
D
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If z(1) = 1 , z(2) = i and A = Arg (z(1) z(2)) B = Arg ((z(1))/(z(2)...

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  2. The descending order of the principal values of arguments of the compl...

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  3. If x(n) + iy(n) = (1 + i)^(n) then x(n - 1) y(n) - x(n) y(n- 1) =

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  4. If x=-5+4i then x^4+9x^3+35x^2-x+4=

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  5. If x is a fifth root of unity then 1 + x + x^(2) + …x^(100)

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  6. If omega = sqrt(z^(2) - 1) where omega is a cube root of unity and z =...

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  7. If x(n) = omega^(n) + (1)/(omega^(n)) then x(1) x(2) x(3)…, x(12) =

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  8. If three complex number are in A.P then they lie on

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  9. The maximum value of |3z + 9 - 7i| if |z + 2- i| = 5 is

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  10. I: The modulus of (sqrt3 + i)/((1 + i) (1 + sqrt3i)) is (1)/(sqrt2) ...

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  11. I: If a and b are positive real numbers then sqrt(-a) xx sqrt(-b) = -s...

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  12. I : The number of solutions of the equation z^(2) + |z|^(2) = 0 is 2 ...

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  13. z(1) = 1 +i , z(2) = -sqrt3 + i , z(3) = 1 + sqrt3i , z(4) = 1 - i A...

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  14. Match the following:

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  15. (A) : The mod amplitude form of (1 + 7i)/((2- i)^(2)) is sqrt2 c is (3...

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  16. (A) : If |z+ 1| - |z - 1| = (3)/(2) then least value of |z| is 3/4 (...

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  17. ((1+i)/(1-i))^4+((1-i)/(1+i))^4=

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  18. If a complex number z satisfies |z|^(2)+1=|z^(2)-1|, then the locus of...

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  19. For all complex numbers z(1) , z(1) satisfying |z(1)| = 12 and |z(2) -...

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  20. If |z + 2i| le 1 and z(1) = 6-3i then the maximum value of |iz + z(1) ...

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