# 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