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!
FP1 HELP ARGHHHHHHHHHHHHHH! Complex numbers loci question Watch
- Thread Starter
- 19-01-2010 11:45
- 19-01-2010 12:24
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
- 19-01-2010 13:09
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)
Now use pythagoras theorem
So combining the two we get
Full answer therefore
hope that makes some sense!