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Magazine Problem 1
In Problems 1-10, find the image of the given set under the reciprocal mapping \(w=1 / z\) on the extended complex plane.the circle \(|z|=5\)
Problem 1
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 \(f\).\(f(z)=2 z-i\)
Problem 1
Find the image of the given set under the mapping \(w=z^{2}\). Represent the mapping by drawing the set and its image.the ray \(\arg (z)=\frac{\pi}{3}\)
Problem 2
Find the image of the given set under the reciprocal mapping \(w=1 / z\) on the extended complex plane.the semicircle \(|z|=\frac{1}{2}, \pi / 2 \leq \arg (z) \leq 3 \pi / 2\)
Problem 2
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 \(f\).\(f(z)=z^{3}\)
Problem 2
Find the image of the given set under the mapping \(w=z^{2}\). Represent the mapping by drawing the set and its image.the ray \(\arg (z)=-\frac{3 \pi}{4}\)
Problem 2
Evaluate the given complex function \(f\) at the indicated points.\(\begin{array}{llll}f(z)=-z^{3}+2 z+\bar{z} & \text { (a) } i & \text { (b) } 2-i & \text { (c) } 1+2 i\end{array}\)
Problem 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 \(2.14\).\(f(z)=z+2-i\)
Problem 3
Find the image of the given set under the reciprocal mapping \(w=1 / z\) on the extended complex plane.the semicircle \(|z|=3,-\pi / 4 \leq \arg (z) \leq 3 \pi / 4\)
Problem 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 \(f\).\(f(z)=\overline{1-z^{2}}\)
