M135W09A9

# M135W09A9 - standard form and plot each of these along with...

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MATH 135 Winter 2009 Assignment #9 Due: Wednesday 1 April 2009, 8:20 a.m. Hand-In Problems 1. If p = 251, q = 281 and e = 73, Fnd the associated RSA public and private keys. 2. (a) In an RSA scheme, the public key is ( e, n ) = (23 , 19837) and the private key is ( d, n ) = (17819 , 19837). Using the Square and Multiply Algorithm, encrypt the message M = 1975 using the appropriate key. (b) In an RSA scheme, the public key is ( e, n ) = (801 , 1189) and the private key is ( d, n ) = (481 , 1189). Note that 41 is a factor of 1189. Using the Chinese Remainder Theorem, decrypt the cyphertext C = 567 using the appropriate key. 3. If z = 1 + 3 i and w = - 3 + 4 i , calculate the values of each of zw, z + w, z - w, and z w in the
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Unformatted text preview: standard form and plot each of these, along with z and w , in the complex plane. 4. Solve the equation 2 z 2 + 2 iz-1 = 0 5. (a) Convert-3 √ 7-√ 21 i to polar form. (b) Convert (12 ,-31 π/ 6) to standard form. 6. Determine the modulus and argument of (1-i ) 42 . 7. Determine all z ∈ C such that z 4 + (1 + 8 i ) z 2 + 8 i = 0. Plot your solutions on the complex plane. Recommended Problems 1. Text, page 180, #3 2. Text, page 181, #19 3. Text, page 181, #21 4. Text, page 218, #16 5. Text, page 218, #32 6. Text, page 219, #44 7. Text, page 219, #51 8. Text, page 219, #65 9. Text, page 222, #122...
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## This note was uploaded on 11/25/2010 for the course MATH 135 taught by Professor Andrewchilds during the Winter '08 term at Waterloo.

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