Sheet 5 week 6 2009 pdf - Tim Stokes Yuri Litvinenko PDF

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Tim Stokes
Yuri Litvinenko...

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Sheet 5

(for Week 6)

MATH102B Introduction to Algebra (2009) Numbers refer to exercise problems in the back of the Lecture Notes booklet.

Practice problems: 1.

(a) Find the general solution of the Diophantine equation 231x + 70y = 28. (b) Hence find the general solution of the Diophantine equation 231x − 70y = 28. (In the same way, one can solve any Diophantine equation of the form ax + by = k, where a, b, k are any integers.)

2. Let z1 = 2 − 3i and z2 = −2 − i. Give the following in rectangular form. (a) z1 − z2 (b) z¯1 (c) |z1 | (d) z 22 = z2 × z2 (e) z2 /z1 3. Solve the following equation for z : 2 + 2i + (3 − i)z = −1 + 2i.

Assignment 5 problems: (Hand in to tutors’ boxes by 5pm, Friday 21 August.) 1. Find the general solution of the Diophantine equation 77x + 363y = 22. 2. Question 31 (a) to (d) inclusive, so not (e) or (f). Interpret “simplify” to mean “give the rectangular form of”....