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If z is a complex number satisfying the ...

If z is a complex number satisfying the relation `|z+1| = z + 2 (1 +i)` , then z is

A

`(1)/(2) ( 1+ 4i)`

B

`(1)/(2) (3 + 4i)`

C

`(1)/(2) (3- 4i)`

D

`(1)/(2) (1 - 4i)`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If z is a complex number satisfying z^(4) + z^(3) + 2z^(2) + z + 1 = 0...

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  2. The complex number z satisfying z^(2) + |z| = 0 is

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  3. If z is a complex number satisfying the relation |z+1| = z + 2 (1 +i) ...

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  4. If z(1) , z(2) are conjugate complex numbers and z(3) , z(4) are also ...

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  5. If z(z), z(2) are two non-zero complex numbers satisfying |z(2)+z(2)|=...

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  6. If |z(1) + z(2)| = |z(1) - z(2)| then the difference in the arguments ...

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  7. The mod-amplitude form of (1 + 7i)/((2 - i)^(2)) is

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  8. The mod -amplitude form of 1+itan theta is

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  9. Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then...

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  10. If (a(1) + ib(1)) (a(2) + ib(2)) … (a(n) + ib(n)) = A + iB then Tan^...

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  11. If z and omega are two non-zero complex numbers such that |zomega| =1...

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  12. If z is a complex number of unit modulus and argument theta then, arg ...

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  13. sqrt(4ab - 2i (a^(2) - b^(2) ) =

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  14. x + isqrt(x^(4) + x^(2) + 1)) =

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  15. If sqrt(x+ iy) = pm (a + ib) then sqrt(x-iy) =

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  16. (1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega...

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  17. If omega is a imaginary cube root of unity , then 225 + (3 omega + 8 o...

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  18. (1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + ...

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  19. If omega is a complex cube root of unity , then (x + 1) ( x + omega) (...

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  20. If 1 , omega , omega^(2) are the cube roots of unity , then (x + y + z...

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