A root of x^5-32 =0 lies in Quadrant II. Write this root in polar form.
Wouldn't the root be 2,0? so it would be 2cis____ but how do you get the degree?

Question

A root of x^5-32 =0 lies in Quadrant II. Write this root in polar form. 
Wouldn't the root be 2,0? so it would be 2cis____ but how do you get the degree?

hartnn · Answer

2,0 is on x axis, its not on Q II

hartnn · Answer

you know how to find 5th roots of unity ?

hartnn · Answer

x^5 = 32 will have 5 roots, one in x axis, 2,0
and other 4 each on one Quadrant

hartnn · Answer

ofcourse, all those 4 roots are complex.

anonymous · Answer

5th root of unity?

anonymous · Answer

You can use DeMoivre's Theorem to figure out these roots.

$\left[32\text{cis}\left(0\right)\right]^{\frac{1}{5}} = 32^{\frac{1}{5}}\text{cis}\left(\frac{0+2\pi k}{5}\right)$

which = 2 cis(72 degrees * k)
Evaluate for k = 0,1,2,3,4 to find all five roots. But you only need the one in Q2. So which angle that is a multiple of 72 degrees is in QII? How about 2*72 = 144 degrees.
So this root would be 2cis(144 degrees) or 2 cis(4pi/5) which is approximately -1.62 + 1.18i