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6 Calculate [√6 (cos+ i sin)] and express the answer in simplest polar form with the argument from 0 ≤ 0 < 2T. COS +i sin πT Submit Answer

6 Calculate [√6 (cos+ i sin)] and express the answer in simplest polar form with the argument from 0 ≤ 0 < 2T. COS +i sin πT Submit Answer

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Calculate the expression \[ \left[ \sqrt{6} \left( \cos \frac{\pi}{5} + i \sin \frac{\pi}{5} \right) \right]^6 \] and express the answer in simplest polar form with the argument from \(0 \leq \theta < 2\pi\). ### Solution Format To input your answer, use the form: \[ \text{Blank} \left( \cos \text{Blank} + i \sin \text{Blank} \right) \] ### Explanation To solve this problem: 1. Identify the modulus and argument of the complex number inside the brackets. 2. Apply the given exponent to both the modulus and argument. 3. Write the resulting complex number in polar form, ensuring the argument lies within the specified range. ### Answer Submission Fill in the appropriate values and use the provided buttons to input square roots and \(\pi\). After completing the fields, click "Submit Answer" to check your solution.
Transcribed Image Text:### Problem Calculate the expression \[ \left[ \sqrt{6} \left( \cos \frac{\pi}{5} + i \sin \frac{\pi}{5} \right) \right]^6 \] and express the answer in simplest polar form with the argument from \(0 \leq \theta < 2\pi\). ### Solution Format To input your answer, use the form: \[ \text{Blank} \left( \cos \text{Blank} + i \sin \text{Blank} \right) \] ### Explanation To solve this problem: 1. Identify the modulus and argument of the complex number inside the brackets. 2. Apply the given exponent to both the modulus and argument. 3. Write the resulting complex number in polar form, ensuring the argument lies within the specified range. ### Answer Submission Fill in the appropriate values and use the provided buttons to input square roots and \(\pi\). After completing the fields, click "Submit Answer" to check your solution.
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