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Edexcel P6 Rev. exe. Qn 34 & 27(b)(transformation), pg 169-170. watch

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    hey guys how is p6 coming along?
    having major problems with transformations. would be grateful if i could get the solutions to them. thanks.
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    If you post some specific questions I'd be glad to help
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    Here's 34:

    Let z=x+iy, then:
    w = [x+(y-1)i]/(x+iy)
    |w|² = [x²+(y-1)²]/(x²+y²)

    The line Im(z)=0.5 mean x=0 and y=0.5. So:
    |w|² = (-0.5)²/(0.5)²
    |w| = 1, as required.

    For the second part:
    w = 2[(z-i)/z] + (3-i) gives the required transformation.

    And for question 27b:
    x = x
    4x = y
    3x = z

    So the vector v=\lambda \left(\begin{array} 1 \\ 4 \\ 3 \end{array}\right) represents this line.

    We want to find a vector x, such that:
    Ax = v
    x = A-1 v
    = \frac{\lambda}{7} \left(\begin{array} 5 & 2 & -1 \\ -17 & 3 & 2 \\ 2 & -2 & 1  \end{array}\right) \left(\begin{array} 1 \\ 4 \\ 3 \end{array}\right)
    = \frac{\lambda}{7} \left(\begin{array} 10 \\ 1 \\ -3 \end{array}\right)

    Take y=1, then z=-3=-3y and x=10=10y. Hence the cartesian equations are:
    x/10 = y = -z/3
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    (Original post by dvs)
    Here's 34:

    Let z=x+iy, then:
    w = [x+(y-1)i]/(x+iy)
    |w|² = [x²+(y-1)²]/(x²+y²)

    The line Im(z)=0.5 mean x=0 and y=0.5. So:
    |w|² = (-0.5)²/(0.5)²
    |w| = 1, as required.

    For the second part:
    w = 2[(z-i)/z] + (3-i) gives the required transformation.

    And for question 27b:
    x = x
    4x = y
    3x = z

    So the vector v=\lambda \left(\begin{array} 1 \\ 4 \\ 3 \end{array}\right) represents this line.

    We want to find a vector x, such that:
    Ax = v
    x = A-1 v
    = \frac{\lambda}{7} \left(\begin{array} 5 & 2 & -1 \\ -17 & 3 & 2 \\ 2 & -2 & 1  \end{array}\right) \left(\begin{array} 1 \\ 4 \\ 3 \end{array}\right)
    = \frac{\lambda}{7} \left(\begin{array} 10 \\ 1 \\ -3 \end{array}\right)

    Take y=1, then z=-3=-3y and x=10=10y. Hence the cartesian equations are:
    x/10 = y = -z/3
    dvs, you are a life saver, thanks loads
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    (Original post by tedd3h)
    If you post some specific questions I'd be glad to help
    its in the heinmann modular books for edexcel AS andA level. if you don't have them i would be happy to post them (questions).
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    Q27b attached.
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