What are the four roots of the following complex polynomial?: P(z) = z^4 - 2z^2 + 4

1 Answer

Answer:

#z = pm sqrt6/2 pm i sqrt(2)/2#

Explanation:

#z^4 - 2 * z^2 + 4= 0#

#Delta = 4 - 4 * 1 * 4 = -12#

#z^2 = (2 pm 2 i sqrt 3)/2#

#z^2 = 2(1/2 pm i sqrt 3/2)#

#z^2 = 2(cos frac{pi}{3} pm i sin frac{pi}{3})#

#z = pm sqrt2(cos frac{pi}{6} pm i sin frac{pi}{6})#

#z = pm sqrt2(sqrt3/2 pm i/2)#

#z = pm sqrt6/2 pm i sqrt(2)/2#