５．All coordinates of the plane change

　We changed various figure in the complex number plane. Next, consider what happens when the whole plane is changed. We try to tranform all straight lines that are parallel and perpendicular to the real axis. This grid figure is changed by the function w=z².
　It becomes a set of parabola which make the origin a focus and there are pseudo-axis int the real plane associated with these parabola.

	⇒
It changes the whole plane in w=z².

　Then, in the other change, it will be how. Let's try to change typical one.


The change of w=1/z		The change of w=√z

The change of w=1/z²		The change of w=e^z

　The characteristic of these complex changes are that the corner between any insecting perpendicular curves even after both curves have been changed.
　The corner made by the intersection of two curves means the corner of the tangent in the point of intersection . Such a change is called " the conformal representation ".
　Because it changed rectangular coordinates, the corner of the curve after the change becomes 90 degrees.

　However, it is always not the conformal representation in all points. The figure on the right is changed by the function w=z².
　In the origin, the corner formed by the intersection of 2 curves is not 90 degrees. It is 180 degrees.

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