# Linear Transformations: Polar and Rectangular Coordinates

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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).

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#### Solution Summary

The region onto which a half plane is mapped is found and discussed. The solution is detailed and well presented.

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