# §4.3 Graphics

## §4.3(ii) Complex Arguments: Conformal Maps

Figure 4.3.2 illustrates the conformal mapping of the strip $-\pi<\imagpart{z}<\pi$ onto the whole $w$-plane cut along the negative real axis, where $w=e^{z}$ and $z=\mathop{\ln\/}\nolimits w$ (principal value). Corresponding points share the same letters, with bars signifying complex conjugates. Lines parallel to the real axis in the $z$-plane map onto rays in the $w$-plane, and lines parallel to the imaginary axis in the $z$-plane map onto circles centered at the origin in the $w$-plane. In the labeling of corresponding points $r$ is a real parameter that can lie anywhere in the interval $(0,\infty)$.

## §4.3(iii) Complex Arguments: Surfaces

In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase. See also About Color Map.