need help in practice test (#44 ETS math subj. test booklet)

Forum for the GRE subject test in mathematics.
hoicow
Posts: 1
Joined: Wed Jul 23, 2008 10:52 am

need help in practice test (#44 ETS math subj. test booklet)

Postby hoicow » Wed Jul 23, 2008 11:01 am

Can someone help me with #44 in the ETS math subj practice test?

#44
if Z=e^(2*pi*i/5)
1+Z+Z^2+Z^3+5*Z^4+4*Z^5+4*Z^6+4*Z^7+4*Z^8+5*Z^9=?

the answer is -5e^(3*pi*i/5)

but I can't get it...hope someone here can help~ THx a lot~

mathsubboy
Posts: 11
Joined: Sun Jul 20, 2008 12:11 pm

Postby mathsubboy » Thu Jul 24, 2008 10:13 am

note that:
Z^5=1;
Z^6=Z;
Z^7=Z^2
Z^8=Z^3
Z^9=Z^4

so

1+Z+Z^2+Z^3+5*Z^4+4*Z^5+4*Z^6+4*Z^7+4*Z^8+5*Z^9

=5*(1+Z+Z^2+Z^3+Z^4)+5*Z^4

=5*Z^4

=the answer




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