To find: The roots of the cube root of
Answer to Problem 40E
The roots of the cube root of
Explanation of Solution
Theorem used:
Roots of a
Let
Calculation:
Rewrite the complex number
The polar form of the complex number
Consider the complex number
Obtain the argument of the complex number
Thus, the argument of the complex number
Obtain the modulus of the complex number
Thus, the value of
Therefore, the polar form of the complex number
By the above theorem, the roots of the cube root of
Use online calculator to sketch the roots in the complex plane as shown below in Figure 1.
From figure 1, it is observed that all cube root of i form a triangle on complex plane.
Chapter I Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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