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FP1 further maths complex numbers question watch

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    (Original post by adriannala)
    Another question, if we are given that |z-2-2i|=2 and arg(z-2-2i)=pi/6 how do we find the value for z in the form a+ib? Thanks.
    Just draw the circle, draw on the line of the argument from the centre of the circle, then work out the point of intersection between the two using Pythagoras. You can deduce the general formula in these situations yourself.
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    Also, how would I solve the question: 'for the transformation w=z-1+2i sketch on separate Argand diagrams the locus of w when:

    c) z lies on the line with equation y=2x+1

    -> why does it cross at (-2, 0) and (0, 4)?? as these do not fit the equation y=2x+1...

    ??
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    (Original post by adriannala)
    Also, how would I solve the question: 'for the transformation w=z-1+2i sketch on separate Argand diagrams the locus of w when:

    c) z lies on the line with equation y=2x+1

    -> why does it cross at (-2, 0) and (0, 4)?? as these do not fit the equation y=2x+1...

    ??
    It doesn't have to cross those coords since you're TRANSFORMING that eq, so coords in the uv-plane wont work on the eq in the xy-plane. That said, are you sure those are the coordinates...? Following the procedure we get something slightly different.

    Say z=x+iy and w=u+iv
    Then we have w=(x-1)+(y+2)i thus u=x-1 and v=y+2. So, if our line y=2x+1 crosses at (-\frac{1}{2},0), (0,1) on the xy plane, then it must cross (-\frac{3}{2},2) and (-1,3) on the uv plane.

    Anywho, you simply need to sub in x(u) and y(v) into the equation y=2x+1, and simplify to get an equation in uv. However, while it satisfies the conditions we deduced above, it does not satisfy those points that you said.
 
 
 
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