How do you:
1. Find all the fifth roots of -1.
2. Find all the third roots of 2+2i
3. Find all the fifth roots of 1 and deduce that:
1 + (2*cos(2*Pi/5)) + (2*cos(4*Pi/5)) = 0.
Help will be very much appreciated.
other exponents will also give -1. you should be able to figure them out easily.
for number two write the complex number as then solve as you did for number one.
for 3 find the roots using a method simmilar to that used for question 1 and you may identify a geometric series.
Yes it would. For a method of finding all 5 of the complex roots, see soroban's excellent post (you may need to google de moivres theorem if you haven't seen this kind of question before).Wouldn't -1 be a root? (for the 1st question)