know from Algebra II that every equation of power 2 has 2 solutions and
equation of power 3 has 3 solutions etc, etc ad nauseum. But up
now, we have only one solution for the equation x3 =
The only one you could find was x =2. Where are the other
We know they exist, but how do you find them. If we extend De
to find roots, suprise!! We can find the missing roots!!
you might ask? Good question! I guess I will show
on to your hat and off we go!
Important definition ( This means pay
The n nth roots of z = r cis 0 are:
z1/n = r1/n cis ( 0/n
+ k . 360o /n) for k = 0, 1, 2, 3, ... n-1
Say what? What are you trying to tell me? Here's
the deal! Say you want to find the 3 cubed roots of 8. That
is x3 = 8. Change 8 into r cis 0.
You remember that right!
8 is on the x-axis so r cis 0 = 8 cis 0o.
Since we are working with the third power, k will equal 0, 1, and
2. Look at the formula! The highest k goes to is n-1.
Tada! Now plug and chug! One at a time.