To find: The roots of the eighth root of 1 and sketch the roots in the complex plane.
The roots of eighth root of 1 are where .
Roots of a complex number:
Let and n be a positive integer. Then has the distinct nth roots where .
Rewrite the complex number 1 in polar form.
The polar form of the complex number is where and .
Consider the complex number 1.
Obtain the argument of the complex number 1.
Thus, the argument of argument of the complex number 1 is
Obtain the modulus of the complex number 1.
Thus, the value of .
Therefore, the polar form of the complex number 1 is .
By the above theorem, the roots of eighth root of 1 are where .
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 roots of eighth root of 1 form a circle on complex plane.
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