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# FP1 HELP ARGHHHHHHHHHHHHHH! Complex numbers loci question watch

1. 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
Attached Files
2. fp1 question.doc (40.0 KB, 114 views)
3. 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
4. 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

implies

therefore

Now use pythagoras theorem

So combining the two we get

implies

P =

hope that makes some sense!

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