Question

What will be the image of straight line y=5 under the function w=e^z. Also find the image of the right half plane under the same function

Answer 1

Answer:

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Answer 2

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The first transformation g(z) is an inversion with respect to the unit circle |z|=1. That is, the image of a nonzero point z is the point g(z) with the properties

which establishes a one to one correspondence between the nonzero points of the z and w planes. Since zz¯¯¯=|z|2, the mapping can be described by means of the successive transformationsWhat will be the image of straight line y=5 under the function w=e^z. Also find the image of the right half plane under the same functionConsider the equation

Thus the points exterior to the circle |z|=1 are mapped onto the nonzero points interior to it, and conversely. Any point on the circle is mapped onto itself. The second transformation f(z)=g(z)¯¯¯¯¯¯¯¯¯ is simply a reflection in the real axis.