Complex numbers

[RobertDyd]

Hi,

One question I dont understand from my textbook is:
Find the product of the five 5th roots of (1+sqrt(2)i)^3
In the answers they just show "-5 + sqrt(2)i " I am confused as to how they got this (unless its through just inputting the question into the calculator and getting an answer), and also what does "five 5th roots" mean, maybe Im just getting my terminology mixed up here idk

Thanks
Robdog

[Quantum44]

Hi,

One question I dont understand from my textbook is:
Find the product of the five 5th roots of (1+sqrt(2)i)^3
In the answers they just show "-5 + sqrt(2)i " I am confused as to how they got this (unless its through just inputting the question into the calculator and getting an answer), and also what does "five 5th roots" mean, maybe Im just getting my terminology mixed up here idk

Thanks
Robdog

I assume they mean:

Solve z^5 = (1 + sqrt(2)i)^3 using de moivres theorem then multiply all the five solutions together to get the answer.

[jakesilove]

I assume they mean:

Solve z^5 = (1 + sqrt(2)i)^3 using de moivres theorem then multiply all the five solutions together to get the answer.

Yep I reckon this is correct! Let us know if you struggle to solve the above equation