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Linear Transformations: Polar and Rectangular Coordinates

3. Find the region onto which the half plane y > 0 is mapped by the transformation

w = (1+ i)z

by using (a) polar coordinates; (b) rectangular coordinates. Sketch the region.

Ans. v > u.

(This problem is from Linear Transformations.)

(Please try to draw the graph clearly. Thank you.)

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The region onto which a half plane is mapped is found. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.