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Math Help - complex number properties

  1. #1
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    complex number properties

    i made this example up...probably wont be nice solutions just want the general method.

    |z-4|=3 and |z|=5 rt(10) how would i find where they intersect

    i thought about substituting z=x+iy and finding x and y but im sure theres easier more general way?
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  2. #2
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    Quote Originally Posted by skystar View Post
    i made this example up...probably wont be nice solutions just want the general method.

    |z-4|=3 and |z|=5 rt(10) how would i find where they intersect

    i thought about substituting z=x+iy and finding x and y but im sure theres easier more general way?
    |z-4|=3 is a circle of radius 3 and centre at (4, 0).

    |z|=5 rt(10) is a circle of radius 5 rt(10) and centre at (0, 0).

    This lets you easily write down the Cartesian equation of each. Solve those equations simultaneously.

    Off hand, I'd say the circles don't intersect ....
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  3. #3
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    tis what i thought i was just getting nasty roots for the real question i thought maybe there was a way of saying |z|=rt(zzbar) e.t.c thanks
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