Concept explainers
To solve: the equation.
Answer to Problem 94E
These six
Explanation of Solution
Given:
Calculation:
The equation can be written as
Use the Rule of nth Roots of Complex Numbers. This rule states:
If
Let's begin by using two formulas,
in order to write our complex number in polar form. Our complex number is
The radius/modulus is
Now, let's find
Choose this value of theta because our complex number point straight along the positive real axis. Using these values of
Now, apply Rule of nth Roots of Complex Numbers to this
Applying this formula with
Thus,
Now, let
Continue by finding all the roots.
To sum up these results in a more compact form, the six roots of 1 are
These six complex numbers are the solutions to the original equation.
Conclusion:
These six complex numbers are the solutions to the original equation.
Chapter 8 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning