Consider the complex number z = 27i. What are the characteristics of the cube roots of z?

Use the drop down menus to complete each sentence.

The cube roots are located on a circle with center at the origin and radius of
.

The cube roots have arguments which differ by
Pi over 3.

The cube roots are located on a circle with a center at the origin and a radius of 3. The cube roots have arguments that differ by 2 Pi over 3.

What is the complex number?

A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.

The given complex number as;

z = 27i

The radius of the cube root is found as;

r=∛x

r=∛27

r=3

The cube roots are located on a circle with a center at the origin and a radius of 3 units.

The argument of a complex number,z=a+ib is;

Θ = tan⁻¹(b/a)

The argument of a complex number z=0+27i

Θ = tan⁻¹(27/0)

Θ = π/2

The cube roots have arguments that differ by 2 Pi over 3.

Hence, the correct answer for the drop-down menu will be 3 and 2.

To learn more about the complex number, refer to the link;

https://brainly.com/question/10251853

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Consider the complex number z = 27i. What are the characteristics of the cube roots of z? Use the drop down menus to complete each sentence. The cube roots are located on a circle with center at the origin and radius of . The cube roots have arguments which differ by Pi over 3.

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What is the complex number?

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Consider the complex number z = 27i. What are the characteristics of the cube roots of z?

Use the drop down menus to complete each sentence.

The cube roots are located on a circle with center at the origin and radius of
.

The cube roots have arguments which differ by
Pi over 3.