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A single branch of the complex logarithm. The hue of the color is used to show the argument of the complex logarithm. The brightness of the color is used to show the modulus of the complex logarithm. The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln(x) around the z-axis.
Window box in Charleston, South Carolina. A window box (sometimes called a window flower box or window box planter) is a type of flower container for live flowers or plants in the form of a box attached on or just below the sill of a window. It may also be used for growing herbs or other edible plants.
In particular, a branch of the logarithm exists in the complement of any ray from the origin to infinity: a branch cut. A common choice of branch cut is the negative real axis, although the choice is largely a matter of convenience. The logarithm has a jump discontinuity of 2 π i when crossing the branch cut. The logarithm can be made ...
The branch point for the principal branch is at z = − 1 / e , with a branch cut that extends to −∞ along the negative real axis. This branch cut separates the principal branch from the two branches W −1 and W 1. In all branches W k with k ≠ 0, there is a branch point at z = 0 and a branch cut along the entire negative real axis.
Flower boxes may also be used to line decks, patios, porches, steps, and sidewalks and they can even be hung from railings. [1] Wood, brick, metal, fiberglass and cellular PVC can all be used in flower box construction, with wood being a classical material of choice. A typical wooden container will last 3–5 years before showing signs of rot.
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