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Homework 2 (MATH 1199 Fall 2019)
1. In the following problems, write in polar form and multiply z1 and z2, and then express that product in the form a+bi, where a,bR.
(a) z1=2+2i and z2=3i
(b) z1=3i and z2=5
(c) z1=1i and z2=5+5i
(d) z1=3i and z2=4i

2. Find Arg(2i1+i) in any way you like.

3. Compute by hand and express the final answer in the form a+bi for a,bR.
(a) (1+3i)14
(b) (223i)11
(c) (44i)11

4. Find all fifth roots of 1.

5. Find all sixth roots of 1.

6. Find all cube roots of i and write them in the form a+bi for a,bR.

7. Find all fourth roots of 1+i.

8. Find all cube roots of 3i.

9. Find all fourth roots of 1 and write them in the form a+bi for a,bR.

10. Write the described function in the form u+iv where u,v:R×RR.
(a) {f:CCf(z)=z22¯z
(b) {g:C{1}Cg(z)=zz+1
(c) {h:C{1+i}Ch(z)=z2z1i
(d) {:C{0}C(z)=¯z|z|