| Yon | so the theta would be ??? |
| happytron | so the angle of -1 is pi, right? |
| Yon | yeh i assume so |
| happytron | well don't assume =] |
| Yon | it is :p |
| happytron | if you don't understand, i'll try to explain more |
| Yon | so how did you come up with the -1? |
| happytron | we want to find theta so that cis( 4*theta) = -1 because, we nkow that (r cis(theta) )^4 = -10 |
| Yon | oh i get you |
| happytron | so the set of complex numbers of the form cis(theta) is a circle in the complex plane with radius 1, centered at the origin |
| Yon | true that, but i just need to find the roots |
| happytron | well, you need to get the geometry then it will be clear... |
| Yon | yeh i understood that much, and every root has to be evenly spaced along the plane |
| happytron | around the circle |
| Yon | so an angle of pi/2 between each answer? |
| happytron | here is the thing yeah if you have two complex numbers r1 cis( t1) and r2 cis (t2) then there product is r1r2 cis(t1 + t2) so the act of multiplying by r2 cis (t2) is to rotate the first number by an angle t2 and scale it by a factor t2... |
| Yon | ahh |
| happytron | its all geometrical |
| Yon | so you cant solve it without going to polar? |
| happytron | wouldn't be as clear |
| Yon | but the thing is converting back to rectangular will be a bit interesting. |
| happytron | involves sines and cosines in this case they're relatively simple the short answer is that theta = pi/4 and cos/sin(pi/4) = sqrt(2)/2 |
| Yon | ok yeh |
| happytron | so its not too bad but its kind of important to realize how multiplication has manifested itself as addition |
| Yon | so it would be 10^(1/4)*((sqrt2)/2) + Sqrt(2)/2i) |