(Due Wednesday, Sep 13)

0. Read Boas Ch2, section 1 - 9, find 5 interesting problems there and do it. (copy down the problem, so the grader / reader know which one you are doing).

1. let �=2���/3z=2eiπ/3,

• compute �2,�3z2,z3.
• what is $\log z$? (be aware this is a multivalued function)

2. how many complex solution does �4=−1z4=−1 have? what are they?

3. let �=2���/3z=2eiπ/3. What does ��zi mean? is it multivalued? How about �1/2z1/2?

4. express $\sin (1+2i)$ in terms of exponential. Is it true that sin⁡(�)=��(���)sin(z)=Im(eiz) for all real $z$, for all complex $z$? (corrected, previous question was asking sin⁡(�)=��(���)sin(z)=Re(eiz), which is false even for $z$ real)

5. What is the Laurent expansion (first 3 terms) of cos⁡(�)�zcos(z) around $z=0$? cos⁡(�)sin⁡(�)sin(z)cos(z) around $z=0$?