Use Schwarz-Christoffel Formula to describe the image of the upper half-plane $y \geq 0$ under the conformal mapping $u^{\prime}=f(z)$ that satisfies the given conditions. Do not try to solve for $f(z)$ $f^{\prime}(z)=(z+1)^{-1 / 3}, f(-1)=0$

Suppose that w=f(z) is a conformal mapping at every point in the complex plane. Where is the mapping $w=e^{f(z)}$ conformal?

Use matrices to find (a) $S^{-1}(z)$ and (b) $S^{-1}(T(z))$.

$$T(z)=\frac{i z}{z-2 i}, S(z)=\frac{2 z+1}{z+1}$$

Use matrices to find (a) $S^{-1}(z)$ and (b) $S^{-1}(T(z))$. $T(z)=\frac{z}{i z-1}, S(z)=\frac{i z+1}{z-1}$

In this problem , find the image of the half-planes $x \geq 0$ and $y \leq 1$ under the given linear fractional transformation T. $T(z)=\frac{z-1}{z}$

In this problem , find the image of the half-planes $x \geq 0$ and $y \leq 1$ under the given linear fractional transformation T. $T(z)=\frac{z+i}{z-i}$

In this problem , find the image of the half-planes $x \geq 0$ and $y \leq 1$ under the given linear fractional transformation T.

$$T(z)=\frac{2}{z-\bar{i}}$$

In this problem , find the images of the points $0,1, i$, and $\infty$ under the given linear fractional transformation $T$. $T(z)=\frac{i}{z}$

Use Schwarz-Christoffel Formula to describe the image of the upper half-plane $y \geq 0$ under the conformal mapping $u^{\prime}=f(z)$ that satisfies the given conditions. Do not try to solve for $f(z)$ $f^{\prime}(z)=(z-1)^{-1 / 2}, f(1)=0$

Determine where the complex mapping w=f(z) is conformal.

$$f(z)=z^3-3 z+1$$

Find equations for the indicated lines both in parametric and nonparametric forms.

Through $P_0(1,-2,4)$ and along $\mathbf{v}=(2,3,-5)$.

If n is a perfect number, prove that $\sum_{d \mid n} l / d=2$.

The parametric curve x = 2 cos (-t), y = 2 sin (-t),0 ≤ t ≤ 2π is traced clockwise. Justify your answer.

Find a set of parametric equations to represent the graph of the given rectangular equation using the parameters (a) t = x and (b) t = 2 - x. $y=x^{3}-x^{2}$