William Collins

2022-01-17

My work with complex numbers verified that the only possible cube root of 8 is 2. Determine whether the statement makes sense or does not make sense, and explain your reasoning.

temzej9

Beginner2022-01-18Added 30 answers

Step 1

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

It is given that,''My work with complex numbers verified that the only possible cube root of 8 is 2''

The objective is to check that the sentence make sense or not

Step 3

This given statement does not makes sense

Here DeMoivre's theorem for roots applies to complex numbers in polar form. Thus writing the given term in terms of polar form that is 8 or

There is three cube root exactly of 8. From DeMoivre's theorem for finding complex roots, the cube roots of 8 are

Step 4

The cube roots of 8 are found by substituting 0, 1, 2 for k in the above expression

Thus polar form,

The rectangular form

Step 5

polar form

Rectangular form

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