Vectors and Matrices...?


    Rep:
    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?

    Rep:
    no-one?

    Rep:
    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.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide the button to the right to create your account

    Slide to join now Processing…

: May 22, 2012

Which unis are the poshest?

See what students perceive to be the classiest establishments in Britain

Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.