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How to sketch Re(iz) = 3

  1. Feb 6, 2014 #1
    Hi guys,
    So as title states, how would one sketch Re(iz) = 3? And an explanation would be splendid.

    This is what I thought:

    let z = a + bi
    i(a+bi) = -b + ai

    Therefore: Re(iz) = -b = 3

    So Real axis = -3?

    Or would it be Real axis = 3
    Since iz is an arbitrary complex number and the real part of this arbitrary complex number is 3.
  2. jcsd
  3. Feb 6, 2014 #2


    Staff: Mentor

    What does this mean? What you have found is that if z = a + bi, the condition that Re(iz) = 3 is that z = a - 3i. What does this look like?
    No, the imaginary part has to be -3.
  4. Feb 6, 2014 #3
    Thanks for your reply, though I am still a little confused.

    Could you go through the working please?
  5. Feb 6, 2014 #4


    User Avatar
    Science Advisor
    Homework Helper

    You are drawing a sketch of z, not of iz.

    b is the imaginary part of z.

    Of course -b is also the real part of iz, but you are not drawing a sketch of iz.
  6. Feb 6, 2014 #5


    Staff: Mentor

    What part are you confused about?
    That's not how it works here, as listed in the rules (click Rules & Guidelines, under SITE INFO in the menu bar, especially the section titled Homework Help Guidelines).
  7. Feb 6, 2014 #6
    I think i understand, so would this be correct for the following question:

    Re(z+2) = -1

    -3 in the real axis?
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