SOLUTION: Express 8j^23 - 8(j^3)^2 in rectangular form.

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Question 887044: Express 8j^23 - 8(j^3)^2 in rectangular form.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We will use 

1. j%5E2=-1, 
2. %28-1%29%5EEVEN=1, 
3. %28-1%29%5EODD=-1, 
4. j%5EODD=J%5EEVEN%2Aj, 
5. j%5EEVEN=%28j%5E2%29%5EN

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8j%5E23+-+8%28j%5E3%29%5E2

          We multiply exponents

8j%5E23+-+8j%5E6

          We factor out 8

8%28j%5E23-j%5E6%29

          Break odd power of j into even power times j:
          Write even power as power of jē:

8%28j%5E22%2Aj-%28j%5E2%29%5E3%29

          Write even power as power of jē
          Substitute -1 for jē:

8%28%28j%5E2%29%5E11%2Aj-%28-1%29%5E3%29

          Substitute -1 for jē:
          Use %28-1%29%5EODD=-1

8%28%28-1%29%5E11%2Aj-%28-1%29%29

          Use %28-1%29%5EODD=-1
          Write -(-1) as +1

8%28%28-1%29%2Aj%2B1%29

          Write (-1)*j as -j

8%28-j%2B1%29

          Distribute 8

-8j%2B8

          Write j-term second:

8-8j

Edwin