How do you find the cube root of 81(\cos(\frac{\pi}{12})+i \sin

Rudy Koch

Rudy Koch

Answered question

2022-02-02

How do you find the cube root of 81(cos(π12)+isin(π12))?

Answer & Explanation

Amari Larsen

Amari Larsen

Beginner2022-02-03Added 10 answers

Step 1
343(cos5+isin5),343(cos125+isin125)and 343(cos245+isin245).
Explanation:
(81(cos(π12)+isin(π12))13
=8113(cisπ12)13
343(cis((13(2kπ+π12)),k=0,1,2
=343(cis5,cis125,cis245), using π=180
=343(cos5+isin5)
Step 2
343(cos125+isin125) and
343(cos245+isin245).

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