Find the value of this logarithmic expression involving fifth root of unity. Let &#x03B1;<!-- α

pouzdrotf

pouzdrotf

Answered question

2022-07-10

Find the value of this logarithmic expression involving fifth root of unity.
Let α be the fifth root of unity. We then want to evaluate the expression
log | 1 + α + α 2 + α 3 1 / α |
Thanks in anticipation for your help in solving this!

Answer & Explanation

escampetaq5

escampetaq5

Beginner2022-07-11Added 12 answers

HINT:
1 + α + α 2 + α 3 = 1 α 4 1 α = 1 1 α 1 α  as  α 5 = 1
1 + α + α 2 + α 3 = 1 α α ( 1 α ) = 1 α  as  α 1

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