(i) Find all solutions to the equation 23 = i.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Problem 3 (4)+(4)+(2) points.
(i) Find all solutions to the equation z* = i.
(ii) Consider the map f: C\ {0} → C defined by f(2) = 1/z. Express this map in polar
coordinates. This means if z =
{r, 0} are the polar coordinates of a point z E C, what
are the polar coordinates of the image f(z) = {r', O'}?
(iii) Visualize the map from (ii) by drawing how the circles S(0, r) = {z E c: |2| = r} for
r = 1/4, 1/2, 1, 2, 4 are mapped. Clearly label your picture.
%3D
Transcribed Image Text:Problem 3 (4)+(4)+(2) points. (i) Find all solutions to the equation z* = i. (ii) Consider the map f: C\ {0} → C defined by f(2) = 1/z. Express this map in polar coordinates. This means if z = {r, 0} are the polar coordinates of a point z E C, what are the polar coordinates of the image f(z) = {r', O'}? (iii) Visualize the map from (ii) by drawing how the circles S(0, r) = {z E c: |2| = r} for r = 1/4, 1/2, 1, 2, 4 are mapped. Clearly label your picture. %3D
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