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Math Help - Complex number- finding the least possible value

  1. #1
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    Complex number- finding the least possible value

    find the least possible value of [z+2-sqrt3i] <2. Describe in geometrical terms.
    sqrt= square root - it is the square root of 3.
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  2. #2
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    Quote Originally Posted by kingkaisai2
    find the least possible value of [z+2-sqrt3i] <2. Describe in geometrical terms.
    sqrt= square root - it is the square root of 3.
    Reformulate this question so that it actualy asks something.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by kingkaisai2
    find the least possible value of [z+2-sqrt3i] <2. Describe in geometrical terms.
    sqrt= square root - it is the square root of 3.
    Part of this maybe should be: Describe |z+2-sqrt3i| <2 in geometric terms.

    As before this defines the set of all points in the complex plane interior of a circle of radius 2 centred at -2+i.sqrt(3).

    RonL
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  4. #4
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    Hello, kingkaisai2!

    The problem is badly worded ... it makes no sense.
    I'll take a guess at what you meant . . .

    Also, in all your problems, unless the inequality is \leq
    . . there is no solution.
    Are you sure it's "less than"?


    Find the least possible value of |z| such that |z + 2 - i\sqrt{3}| \:\leq \:2
    Describe in geometrical terms.

    We have: . |z - (-2 + i\sqrt{3})| \:\leq \:2

    This is the set of points within 2 units of -2 + i\sqrt{3}.

    This is the set of points in or on the circle
    . . with center C(-2,\sqrt{3}) and radius r = 2.
    Code:
                              |
                  * * *       |
              *           *   |
            *               * |
           *                 *|
                      _       |
          *      (-2,√3)      *
          *        C*         * 
          *           \       * 
                        \     |
           *              \  *|
            *               o |
         -----*-----------*---+----
                  * * *       |O
                              |

    The point z with the least magnitude
    . . is the intersection of the circle and the line CO.

    The line has the equation: . y \:= \:-\frac{\sqrt{3}}{2}x

    The circle has the equation: . (x + 2)^2 + (y - \sqrt{3})^2\:=\:4


    Find their intersections and take the rightmost point.

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