If z is a complex number having least modulus and |z – 2 + 2i| = 1, then z =

If z is a complex number having least modulus and |z - 2 + 2i| = 1, then z =

  1. A

    (21/2)(1i)

  2. B

    (21/2)(1+i)

  3. C

    (2+1/2)(1i)

  4. D

    (2+1/2)(1+i)

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    Solution:

    We have,

    |z2+2i|=1|z(22i)|=1

    Hence, z lies on a circle having center at (2, -2) and radius 1. It is evident from the figure that the required complex number z is given by the point P.

    We find that OP makes an angle π/4 with OX and

    OP=OCCP=22+221=221

    So, coordinates of P are [(221)cos(π/4), (221)sin(π/4)], i.e., ((21/2),(21/2)).

    Hence,

    z=212+212i=212(1i)

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