Advertisement
If you have a new account but are having problems posting or verifying your account, please email us on hello@boards.ie for help. Thanks :)
Hello all! Please ensure that you are posting a new thread or question in the appropriate forum. The Feedback forum is overwhelmed with questions that are having to be moved elsewhere. If you need help to verify your account contact hello@boards.ie

Complex numbers -- Loci Problems

  • 22-09-2008 10:07PM
    #1
    Closed Accounts Posts: 1,788
    ✭✭✭


    Hi
    From Engineering Mathematics KA Stroud
    See link below , I am having difficulty understanding this problem,
    I don't see where he makes the jump from
    z + 1 = x +jy +1 = (x+1) +jy = r1Ltheta1 = z1

    he is putting it in polar form here ?

    and surely it should be (x+1)Squared - ySQUARED .. as jSQUARED is -1


    People who have the book its 5th ed p. 468




    http://farm4.static.flickr.com/3168/2880405318_00c6d3d1db_b.jpg


Welcome!

It looks like you're new here. Sign in or register to get started.

Comments

  • Registered Users, Registered Users 2 Posts: 1,595 MathsManiac
    ✭✭✭


    I think you can safely ignore the polar stuff that's interspersed with the solution - my guess is that he's including the polar form along the way because sometimes when you express things in polar form the answer just jumps out at you.

    Anyway, to answer your question, the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2. (It's the distance from the point to the origin on an Argand diagram.)

    So, he has just expressed z as x+yj, and then found the relevant moduli in terms of x and y.

    That ok?


  • Closed Accounts Posts: 1,788 jackdaw
    ✭✭✭


    I think you can safely ignore the polar stuff that's interspersed with the solution - my guess is that he's including the polar form along the way because sometimes when you express things in polar form the answer just jumps out at you.

    Anyway, to answer your question, the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2. (It's the distance from the point to the origin on an Argand diagram.)

    So, he has just expressed z as x+yj, and then found the relevant moduli in terms of x and y.

    That ok?

    Sort of... but still why is the y^2 positive, since j^2 is -1 ??


  • Closed Accounts Posts: 773 Cokehead Mother
    ✭✭✭


    "the modulus of a+bj is defined to be a^2 + b^2, not a^2 + (bj)^2."

    So the modulus of (x + 1) + yj is root[(x + 1)^2 + y^2] and not root[(x + 1)^2 + (yj)^2] which would give you -y^2.


  • Closed Accounts Posts: 1,788 jackdaw
    ✭✭✭


    of course!!!


    cheers!


Welcome!

It looks like you're new here. Sign in or register to get started.
Advertisement