Weird polar coordinates question

I have a really weird question in my homework and have no idea how to answer it. I am not looking for an easy answer but I really need help..can someone please explain this to me?? Thanks :)

a)Determine all points in the plane which have the same carthesian as
polar coordinates.


b) Suppose you have a point P in the plane, which makes an angle  with
the x-axis. Furthermore, the distance of P to the origin is (theta)/(Tan( theta)). Show
that its polar coordinates (r, theta) are a multiple of the carthesian coordi-
nates (a, b) (i.e. there exists some elements of R such that (lamda a, lamda b) = (r, theta).

....WHAT??? Please help me how do you do this?? And thank you so much. ^^

Hello,

a)= = = = = = = = = = = = = = = = = = = = =
In the complex plane, any point z can be described either in cartesian coordinates or in polar coordinates.
{ z = x + iy
{ z = |z|.exp(iθ)

All points in the plane which have the same carthesian as
polar coordinates would then have:
{ x = |z| = √(x² + y²)
{ y = θ

x ≥ 0
x = √(x² + y²)
x² = [√(x² + y²)]²
x² = x² + y²
0 = y²
0 = y

Hence, the solution is:
{ x ≥ 0
{ y = θ = 0

Then all the points in the plane which have the same carthesian as
polar coordinates the half x-axis describing the positive reals.

a) you would have to make some assumptions.

Cartesian = (X, Y)
Polar = R ∠θ

Thus assume X = R and Y = θ

You will have to pick arbitrary units for θ. The mathematical choice would be radians.

Now use Pythagoras to set up some equations that link X, Y, R and θ

I haven't looked at b) because it made me go dyslexic.