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

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To solve the equation z^3 = -8i, it is suggested to express -8i in polar form using De Moivre's theorem. The polar form is derived as r*e^(i*theta), where r is the modulus and theta is the argument. After converting -8i, the solution involves taking the cube root and considering all possible angles around the unit circle. The discussion highlights that while De Moivre's theorem is applicable, there are simpler methods to arrive at the solution. Overall, the focus is on finding the cube roots of the complex number effectively.
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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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