To find: The roots of the fifths root of 32 and sketch the roots in the complex plane.
Answer to Problem 38E
The roots of fifth root of 32 are
Explanation of Solution
Theorem used:
Roots of a
Let
Calculation:
Rewrite the complex number 32 in polar form.
The polar form of the complex number
Consider the complex number 32.
Obtain the argument of the complex number 32.
Thus, the argument of the complex number 32 is
Obtain the modulus of the complex number 32.
Thus, the value of
Therefore, the polar form of the complex number 32 is
By the above theorem, the roots of eighth root of 32 are
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 fifths roots of 32 form a polygon on complex plane.
Chapter I Solutions
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