SOLUTION: Find all the values of the following (separate multiple answers with commas): 1. (-256)^1/4 = ? 2. 1^1/5 = ? 3. i^1/4

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find all the values of the following (separate multiple answers with commas): 1. (-256)^1/4 = ? 2. 1^1/5 = ? 3. i^1/4       Log On


   

Question 205835: Find all the values of the following (separate multiple answers with commas):
1. (-256)^1/4 = ?
2. 1^1/5 = ?
3. i^1/4
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. (-256)^1/4 = ?
= 2 x 4th root of -1
---------
2. 1^1/5 = ?
= 1
--------
3. i^1/4
= 8th root of -1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!

1. (-256)^1/4
= [256^(1/4)cis[(180+360n)/4]
= 4cis45,4cis135,4cis225,4cis315
-------------------------------------
2. 1^1/5
= cis[(0+360n)/5]
= cis(0),cis(72),cis(144),cis(216),cis(288)
-----------------------------------------

3. i^1/4
= cis[(90+360n)/4]
=cis(12.5),cis(102.5),cis(192.5),cis(282.5)
=================================================
Cheers,
Stan H.