Question

5.7. Give the normal closures of the following extensions: \( \mathbb{Q}(\sqrt[3]{11}): \mathbb{Q} \) and \( \mathbb{Q}\left(e^{2 \pi i / 3}\right): \mathbb{Q} \).

Name: 5.7. Give the normal closures of the following extensions: ℚ(√(11)): ℚ and ℚ(e^2 π i / 3): ℚ.
Uploaded: 2020-07-12T00:15:37-08:00
Duration: 1 min 34 s
Channel: Zachary Mitchell
Description: 5.7. Give the normal closures of the following extensions: ℚ(√(11)): ℚ and ℚ(e^2 π i / 3): ℚ.

          5.7. Give the normal closures of the following extensions: \( \mathbb{Q}(\sqrt[3]{11}): \mathbb{Q} \) and \( \mathbb{Q}\left(e^{2 \pi i / 3}\right): \mathbb{Q} \).

Added by Kimberly R.

Precalculus

David Cohen, Theodore B. Lee, David… 7th Edition

Chapter 10

Instant Answer

Solved by Expert Zachary Mitchell

07/12/2020

Step 1

The minimal polynomial is \( x^3 - 11 \). Show more…

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5.7. Give the normal closures of the following extensions: \( \mathbb{Q}(\sqrt[3]{11}): \mathbb{Q} \) and \( \mathbb{Q}\left(e^{2 \pi i / 3}\right): \mathbb{Q} \).