number theory Find all of the primitive roots in Z,.
4. Recall that a € ZnZ is called a primitive root modulo n, if the order of a in Z/nZ is equal to on). We have seen in class that, if p is a prime, then we can always find primitive roots modulo p. Find all elements of (Z/11Z)* that are primitive roots modulo 11. 5. Can you find primitive roots modulo 16? Explain your answer. 6. In class, we found 2 primitive roots modulo 9 = 32, namely 2...
29. Give the number of primitive roots (mod p), where p is a prime. 29. Give the number of primitive roots (mod p), where p is a prime.
3. Supposeis a primitive 12th-root of unity. Then show that ç5,57 and are also primitive 12th-roots of unity
fekri/n k0,1,...,n-1}, called the nth roots of unity. A primitive root of unity is = eri/n for which 2. The roots off(x) = x"-1 are the n complex numbers Cn and are ged(n, k) 1. It is easy to see that Q(C) is the splitting field of zn - 1. (a) For each n 3,... ,8, sketch the nth roots of unity in the complex plane. Use a different set of axes for each n. Next to each root, write...
Find all the roots of w4 = 1-j and draw the roots on an Argand plane.
1) find all value of i^i, and show that they are all real 2) Find all values of log(-1-i) 3) find a) the cube roots of -1 b) the sixth root of i c) the cube roots of 1-i 4) Find (d/dz) i^z
3. Let p>3 be an odd prime and let {ri,r2, .r} be the set of incongruent primitive roots modulo p. Compute the product rir .r modulo p. Recall the proof of Wil- son's Theorem for inspiration 3. Let p>3 be an odd prime and let {ri,r2, .r} be the set of incongruent primitive roots modulo p. Compute the product rir .r modulo p. Recall the proof of Wil- son's Theorem for inspiration
Find all 5th roots of -243i.
find all complex roots of w=125(cos150+i sin150) write the roots in polar form Find all the complex cube roots of w=125( cos 150° + i sin 150°). Write the roots in polar form with in degrees. zo= cos 1°+ i sin º) (Type answers in degrees. Simplify your answer.) z = cos 1° + i sin º) (Type answers in degrees. Simplify your answer.) 22- cosº + i sin º) (Type answers in degrees. Simplify your answer.) Enter your answer...