Hi.

I have some complex numbers

z = r \cdot {e^{i\varphi }}

\varphi \in \left( {0;\frac{\pi }{4}} \right)

r \in \left( {0; + \infty } \right)



and I need to define a function w(z)
which would map everything inside a circle

\left| w \right| < 1



it is also given that

w(0) = 1

w({e^{i\frac{\pi }{8}}}) = 0



How should I approach this? Many thanks.