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There is probably some simple geometric way of doing this - it can't be coincidence that the rayOriginally Posted by Tangera
Hello!
Q: The complex number w is represented by the point of intersection of the loci |z -8 -6i| = 5 and arg(z -4 -3i) = 2, where
(0.75). Find w, in the form x + iy, giving the exact decimal values of x and y.
Thank you for helping!passes through the centre of the circle
and that the terminus of the ray lies on this circle.
But a blunt apporach is:
Get the Cartesian equation of
Get the equation of the line that the raylies on. Note that the gradient of this line is
and it passes through the point (4, 3).
Get the intersection of the circle and the line. The solution you want to keep is the one such that y > 3 (a diagram makes this clear).
