Question

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 pole and radius of . the cube roots have arguments which differ by π over 3.

Answer 1

The drop-down menu will be 3 and 2.

What is the complex number?

• Real and imaginary numbers combine to form complex numbers with two components. Complex numbers serve as the foundation for more complex math, including algebra. They have various practical applications, particularly in electronics and electromagnetism.

The complex number z = 27i.

The radius of the cube root is: $r\sqrt[3]{x}$

                                                  $r\sqrt[3]{27}$

                                                  $r=3$

Cube roots are located in a circle with a center at the origin and a radius of 3 units.

The complex number,z=a+ib is; Θ = tan⁻¹(b/a)

The complex number z=0+27i is:

                                                     Θ = tan⁻¹(27/0)

                                                     Θ = π/2

Cube roots have more than 3 arguments that differ by 2 π.

Therefore, The drop-down menu will be 3 and 2.

To learn more about the complex number, refer to:

brainly.com/question/11089283

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