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Math Help - Complex Numbers: Argand Diagrams

  1. #1
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    Exclamation Complex Numbers: Argand Diagrams

    determine the cartesian form and hence sketch the locus of z
    Re(z)= l z l

    given that l z-1+i l ≤ 1 find
    a) the minimun and maximun value for l z l
    b) the minimun and maximun value for arg (z)

    given that l z-1+i l ≤ 2 and Re (z) ≥ 1 find
    a) min and max value for l z l
    b) min and maz value for arg (z)


    thank you...
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  2. #2
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    Quote Originally Posted by Fibonacci View Post
    determine the cartesian form and hence sketch the locus of z
    Re(z)= l z l

    Mr F says: Let z = x + iy. Post your work if you're still stuck.

    given that l z-1+i l ≤ 1 find

    Mr F says: Do you realise the boundary of this region is a circle with centre at z = 1 - i and radius 1?

    a) the minimun and maximun value for l z l
    b) the minimun and maximun value for arg (z)

    Mr F says: Draw a line from z = 0 that passess through z = 1 - i. You can now use geometrical properties, Pythagoras' Theorem and trigonometry of right-triangles to get these answers.


    given that l z-1+i l ≤ 2 and Re (z) ≥ 1 find
    a) min and max value for l z l
    b) min and maz value for arg (z)

    Mr F says: Consider what I've said above.


    thank you...
    ..
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