# help needed on algebra

• Jan 18th 2009, 01:44 AM
anon18
help needed on algebra
hi i would be very grateful if anyone could help me out with any of the questions

(a) use the definition of addition for rational numbers to verify that it satisfies the commutative and associative laws.
(b)use the definition of mutiplication for complex numbers to verify that it satisfies the commutative and associative laws.
(c)solve the system of linear equations in complex numbers:
(2 + i)x + (-3i)y = 3 + i
3ix + (3 - 2i)y = 3 - 3i
(d)how many complex numbers z are there that z^6=1? Calculate them and sketch the argand diagram.

what i have done so far
(a)
http://upload.wikimedia.org/math/b/9...428a148b89.png well i got this for the definition of addition for rational numbers but i need help for the second part it seems simple yet i cannot manage to do it.
(c) i've been taught how to solve systems in geometry but i cannot solve this.
(d)z=1^(1/6)
z=1
1(cos(theta)+isin(theta)) i don't know how to figure out the angle of theta

if anyone could help with any part i would appreciate it alot
• Jan 18th 2009, 02:51 AM
hmmmm
for part d you must set z^6 -1 equal to one and then find a root the e.g 1
you must then use (z-1) as a root and if that is a root so is its complex conjuate (z+1) you must then use this to form your quadratic factor. Also for complex polynomial it has exactly the same amount of factors as its degree.e.g. six does this help??

for part c is it asking to solve seperately or at once.
• Jan 18th 2009, 03:04 AM
anon18
thank for part (d). for part (c) its asking to solve together, in geometry we were taught how to so it in terms of planes not complex numbers. and you use back substitution or leave it in eshlon form.