(Solved):   7. Determine the image of the ray \( \operatorname{Arg}(\mathrm{z})=\pi / 4 \) under inver ...

 

7. Determine the image of the ray \( \operatorname{Arg}(\mathrm{z})=\pi / 4 \) under inversion mapping. 8. Find the image of the given set under the mapping \( w=\mathrm{z}^{2} \). Represent the mapping by drawing the set and its image i) the polygon with vertices \( 0,1,1+i \), and \( -1+i \). ii) the line \( y=-3 ; f(z)=-z^{2}+i \). 9. Determine the image of the circle \( \left|z+\frac{i}{2}\right|=\frac{1}{2} \) under \( w(z)=\frac{3 i}{z}+1+i \) 10. Under the mapping \( w(z)=2+\frac{1+i}{z} \), find the image of the annulus region \( 1 \leq z \leq 2 \).