91Ó°ÊÓ

Find the image of the given set under the mapping \(w=z^{2}\). Represent the mapping by drawing the set and its image.the line \(x=3\)

Plot the images of the complex numbers \(z=1,1+i, 1-i\), and \(i\) under the given function \(f\) as position vectors, and (b) plot the images as vectors in the vector field associated with \(f\).\(f(z)=\overline{1-z^{2}}\)

Find the image of the closed disk \(|z| \leq 1\) under the given linear mapping \(w=f(z)\) and (b) represent the linear mapping with a sequence of plots as in Figure \(2.14\).\(f(z)=(1+i) z\)

Plot the images of the complex numbers \(z=1,1+i, 1-i\), and \(i\) under the given function \(f\) as position vectors, and (b) plot the images as vectors in the vector field associated with \(f\).\(f(z)=\frac{1}{z}\)

Find the image of the given set under the reciprocal mapping \(w=1 / z\) on the extended complex plane.the quarter circle \(|z|=\frac{1}{4}, \pi / 2 \leq \arg (z) \leq \pi\)

Find the image of the given set under the mapping \(w=z^{2}\). Represent the mapping by drawing the set and its image.the line \(y=-5\)

Evaluate the given complex function \(f\) at the indicated points.\(f(z)=|z|^{2}-2 \operatorname{Re}(i z)+z \quad\) (a) \(3-4 i \quad\) (b) \(2-i \quad\) (c) \(1+2 i\)

Plot the images of the complex numbers \(z=1,1+i, 1-i\), and \(i\) under the given function \(f\) as position vectors, and (b) plot the images as vectors in the vector field associated with \(f\).\(f(z)=z-\frac{1}{z}\)

Find the image of the given set under the reciprocal mapping \(w=1 / z\) on the extended complex plane.the annulus \(\frac{1}{3} \leq|z| \leq 2\)

Find the image of the closed disk \(|z| \leq 1\) under the given linear mapping \(w=f(z)\) and (b) represent the linear mapping with a sequence of plots as in Figure \(2.14\).\(f(z)=2 z-i\)