Show that the locus in the complex plane of all points satisfying #cosv + isinv # where #v in [0,2pi]# is a unit circle?
1 Answer
Oct 5, 2017
Suppose we have a point
# z = cosv + isinv \ \ # where#v in [0,2pi]#
Now let us suppose that
# z = x+iy #
Equating real and imaginary components, we have:
# x=cosv#
# y = sinv #
So, the locus of the point
# x^2 + y^2 = cos^2v+sin^2v = 1 #
Hence the point