Question

simplify (1-i(1/root3))^10 using demoivres theorem
I got to this stage
1024/243 * (cos10pi/6+isin10pi/6) which almost gives me the right answer but it has a negative. and in the answer to the question both complex and real parts are positive

Answer 1

what did you find for the angle?

Answer 2

angle should be \(-\frac{\pi}{6}\) or \(\frac{11\pi}{6}\)
so when you multiply by ten you get \(-\frac{5\pi}{3}\) or \(\frac{\pi}{3}\) which is why both parts are positive

Answer 3

thanks! i've solved it. but why do u say or 11pi/6? why is there two angles?

Answer 4

the angle is not unique when you write \(a+bi=r(\cos(\theta)+i\sin(\theta))\) any coterminal angle will do

Answer 5

ah i see, they both give the same value. Thanks again!

Answer 6

so you can choose \(-\frac{\pi}{6}\) or \(\frac{11\pi}{6}\) or anything coterminal

Answer 7

yw