Complex Roots of Equations: Solving z^3 = -8i

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Homework Help Overview

The problem involves solving the equation z3 = -8i, which falls under the topic of complex numbers and roots of equations.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of De Moivre's theorem and consider alternative methods for solving the equation. There is mention of expressing -8i in polar form and exploring the implications of different angles on the unit circle.

Discussion Status

The discussion is active, with participants sharing different perspectives on how to approach the problem. Some guidance on using polar coordinates and De Moivre's theorem has been provided, but no consensus has been reached regarding the preferred method.

Contextual Notes

There is a repetition of the homework statement, indicating that clarity on the problem setup may be needed. Participants are also reflecting on the effectiveness of various approaches without arriving at a definitive solution.

littlewombat
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De Moivre's theorem~~HELP~

Homework Statement



Solve the following equations


z^3=-8i


Can anyone please tell me how to solve this problem?
 
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You can use De Moivre's theorem (actually, are you meant to?) but there is an easier way to solve it.

Notice that -8i=\left(2i\right)^3
 


littlewombat said:

Homework Statement



Solve the following equationsz^3=-8iCan anyone please tell me how to solve this problem?

Z=cuberoot(-8i)

So write (-8i) in r*e^(i*theta) form and then raise it to the one-third...then consider all the angles that theta could be as you round the unit circle once.

EDIT: I like Mentallic's way, haha.
 


Apphysicist said:
EDIT: I like Mentallic's way, haha.

Haha thanks :approve:
 

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