To find: The roots of the cube root of i and sketch the roots in the complex plane.
The roots of cube root of i 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 i in polar form.
The polar form of the complex number is where and .
Consider the complex number i. Here, . So, , and .
Obtain the argument of the complex number i.
Thus, the argument of the complex number i is .
Obtain the modulus of the complex number i.
Thus, the value of .
Therefore, the polar form of the complex number i is .
By the above theorem, the roots of cube root of i 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 cube root of i form a triangle on complex plane.
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