(a)
To find the indicated roots of the
(a)
Explanation of Solution
Given information:
The given expression is
Using the formula for nth roots of a complex number which states that,
For a positive integer the complex number has exactly distinct roots given by,
Where.
Hence, its modulus is
Its argument is
Thus, the trigonometric form comes out to be
Therefore, the given complex number is
As sine and cosine are negative in third quadrant
Using the above formula,
So, for roots are as follows
For 0,
For 1,
For 2,
(b)
To represent the roots graphically.
(b)
Explanation of Solution
Representing the solution graphically as follows-
(c)
To represent the roots in standard form.
(c)
Explanation of Solution
Writing the roots in standard form as follows-
For the second root
For the third root
Chapter 6 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning