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FP1 HELP ARGHHHHHHHHHHHHHH! Complex numbers loci question Watch

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    I'm stuck on the June 09 paper OCR (MEI) where it asks me to express the complex number represented by the point P in the form a+bj, giving the exact values of a and b. How can I work this out...I don't remember being taught it. I've attached the question.

    Any help would be greatly appreciated!

    Cheers,

    K
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    I may be wrong, but:

    Distance from centre of circle to P = 2. Using a^2 + b^2 = c^2 (where c is the line from the centre to P), a^2 and b^2 are the same, so 2a^2 = 4, a^2 = 2 and a = root 2.

    So the point P would be (4 - root 2), (2 + root 2)j
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    Start from O

    Need to go 4 + 2j to get to the centre of the circle

    Now to get to P from circle centre, have to move radial distance (i.e. 2)

    Can see from diagram that point P sits at exactly 45 degrees from the purely real axis (i.e. a horizontal line)

    use  tan \theta = \frac{imag}{real}

    implies

     \frac{|imag|}{|real|} = tan(45) = 1

    therefore

     |imag| = |real|

    Now use pythagoras theorem

     |imag|^2 + |real|^2 = radius^2 = 2^2 = 4

    So combining the two we get

     |imag|^2 + |imag|^2 = 4

    implies

     |imag| = |real| = \sqrt{2}

    Full answer therefore

    P =  4 - \sqrt{2} + (2 + \sqrt{2})j

    hope that makes some sense!
 
 
 
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