### 20 Chapter in Review Answers to selected odd-numbered problems begin on page ANS-51.

Answer Problems 1–10 without referring back to the text. Fill in the blank or answer true/false.

- Under the complex mapping
*f*(*z*) =*z*^{2}, the curve*xy*= 2 is mapped onto the line _____. - The complex mapping
*f*(*z*) = −*iz*is a rotation through _____ degrees. - The image of the upper half-plane
*y*≥ 0 under the complex mapping*f*(*z*) =*z*^{2/3}is _____. - The analytic function
*f*(*z*) = cosh*z*is conformal except at*z*= _____. - If
*w*=*f*(*z*) is an analytic function that maps a domain*D*onto the upper half-plane*v*> 0, then the function*u*= Arg(*f*(*z*)) is harmonic in*D*. _____ - Is the image of the circle
*z*− 1 = 1 under the complex mapping*T*(*z*) = (*z*− 1)/(*z*− 2) a circle or a line? _____ ...

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