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Math Help - Argand diagrams

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    Argand diagrams

    Draw Argand diagrams to illustrate the (kz)*=kz*where k is a real number and z* means the conjugate of z

    I know I am asking a lot so if you find it to troublesome to "draw" a diagram, can you please thoroughly describe what it looks like.
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    Quote Originally Posted by kingkaisai2
    Draw Argand diagrams to illustrate the (kz)*=kz*where k is a real number and z* means the conjugate of z

    I know I am asking a lot so if you find it to troublesome to "draw" a diagram, can you please thoroughly describe what it looks like.
    On the Argand plane the complex number z = a + ib is simply the coordinate point (a, b). Thus z* = a - ib is the point (a, -b), or the point (a, b) reflected over the "x" (real) axis.

    You can think of the complex numbers as vectors in the Argand plane. So by multiplying z by a real number k you are simply stretching the vector by a factor of k.

    Now it's simply a matter of showing that the operations of stretching and reflecting the vector over the real axis are commutative, which should be obvious.

    -Dan
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