Expert: Scotto - 2/25/2009

Question
Find the fifth roots of the given number in polar form. (List your answers counterclockwise starting at the positive real axis.)

15(cos(pi/2)+isin(pi/2))

What I did was take 5 x pi/2 and got.. pi/10 when k=0.
so i wrote it as:

15(cos (pi/10) +isin (cos(pi/10)))

and so forth with k= 1,2,3,&4.

i got for the angle of
k=1   (pi/2)
k=2   (9pi/10)
k=3    (13 pi/10)
k=4    (17pi/10)

written in polar form as like k=0 above...
what am I doing wrong, since it's not in standard form and is already in polar form, wouldn't i just multiply the root of 5 by the angle???

Am i suppose to add ^5sqrt(15) instead of just 15?? what am I doing wrong.. please help!

Answer
What does ^5sqrt(15) mean?  The 5th root of 15?
The angles you got were correct, but you forgot k=0.

====================================================================

The fifth root of 15 is just the fifth root of 15.

To take the 5th root of the complex number, you need to take the angle plus 0,2π,4π,6π, and 8π and divide by 5.

This will cause us to add 0, 2π/5, 4π/5, 6π/5, and 8π/5 to π/10
sin π/10 is 1/5 of π/2.

Since 10 is the common denominator, we will add π/10 to
0, 4π/10, 8π/10, 12π/10, and 16π/10.

The result will be π/10, 5π/10, 9π/10, 13π/10, and 17π/10.
These are the angles of the five fifth roots.

====================================================================

Yes,  you should take the fifth root of 15.  That can't really
be expressed here on the PC.  It is just the 5th root of 15.
If the 5 could be superscrited, it would be 5√ for the fifth root,
but that looks like 5*squareroot, which it's not.

The angles look right, but there needs to be one more:
k=0: π/10.