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Vectors and Matrices...?

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    Vectors and Matrices
    For z, a 2 C define the principal value of log z and hence of za. Hence find all
    solutions to
    (i) zi = 1
    (ii) zi + z i = 2i ,
    and sketch the curve |zi+1| = 1.

    No idea how to start this question can anybody offer me a hint as to where I should begin?
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    no-one?
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    What do you mean by "a 2 C"?

    As far as I can see the question isn't about vectors, matrices or logs. Sorry if I've got it wrong.

    zi=1 \Rightarrow z=\frac{1}{i} \Rightarrow z=-i.

    zi + zi = 2i \Rightarrow 2zi = 2i \Rightarrow z=1

    The last one is slightly more interesting.

    Can you sketch |w-(-1)|=1?

    Then let w=zi. Multiplication by i gives a 90 degree anti-clockwise rotation.

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Updated: May 22, 2012
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