Let p(x) = 24 + 23 +1€ Z2[2] and let a = [z] in the field E = Z2[z]/(p(x)), so a is a root of p(x). (a) (15 points) Write the following elements of E in the form aa+ba+ca+d, with a,b,c,d € Z2. i. a“, a, a6, and a 10 ii. a5 +a+ + a2 + 1 iii. (a? + 1)4 (b) (5 points) The set of units E* = E-{0} of the field E is a group of order...
Complex Analysis: 1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) Let I = 71+72, where yi and 72 are the directed smooth curves parameterized by TT zi(t) = 2i(1 – 2t), 0 < t < 1 z2(t) = 2eit, 277 < t < 2' respectively. Compute...
Let A = [2-3i 3 + 2i [ 5 - 1+i –1 + i 21 1-11 -1-il -2 ] The set of solutions to the equation Ax = 0 is 22 = [Select] 23+ [Select] 21
give a complex number in trigonometric form z = (-V12 + 2i)(1 + i)(cos 24 – i sin 24) (2+ V12i)(COS 6 + i sin o)
Ifz-I+),22-1-j, and 3=-2, calculate the magnitude and phase (in radians) of (a) zi (b) z2 (c) z3 (d) z1 +z (e) z z3 (f) z1z2 (g) t22 (h) 을 2. 21 23 21-23 Z1
Using complex or magnitude angle math to solve for Z, V or I Let Z1 = (2 + j2) Zg = (1 + j2) Zg = (4 + j2) 11 = (4 + j2) Solve for A) Zi + Za + Zs (Series impedances) B) Zi ll Z2三? (Parallel impedances) C) Il * Z3-) (Ohms Law) D) Vı/Zs-? (Ohms Law)
I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the form a+ ib (c) Z, Z, (b) 22, +Z, (a).
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
#1,5,9 and #13,17,21,25 please. In Exercises 1-12, graph each complex number in the complex plane 3. -2 4i 2 2. 3 5i 7.-3i 8.-5i 6. 7 47 19 7 15 2 11 2 12. 10 10 each complex number in polar form 15. 1 V3i 14. 2 + 2i 16. -3- V3i 3. 1-i 20. -V3+i 18. V5_V5İ 19. V3-3i 17-44i 24. -8-8V3i 22. 2 + Oi 2 23, 2v3-2i 21. 3 +0i V3 1 1 V3 28·16+161 26, 1...
1 1 + COS Z 8. Define the function f(x) = (2 + 1)2( 23 +1) (a) (6 points) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) (6 points) Let I = 71+72, where 71 and 42 are the directed smooth curves parameterized by -TT TT zi(t) = 2i(1 – 2t), 05t51 z2(t) = 2eit, sts 2' respectively. Compute Sr...