Complex number - roots (1 Viewer)

Cujo10

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I do not get how to solve this question from 2-4. Any help?
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shashysha

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I think its essentially asking to find the three cube roots of unity of z=1+i. Convert z=1+i into mod-arg form then using De Moivre's Theorem would he what I'd do.
 

Canteen

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2.


So the "primary root" will be

3. Note that 1/3arg(z) can also take other values namely:

So other roots will be:

4. Convert cis roots to cartesian which will be quite laborious in this instance because the arguments aren't nice so compound/double angle formulae for cos and sin will be required.
 

Canteen

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I think its essentially asking to find the three cube roots of unity of z=1+i. Convert z=1+i into mod-arg form then using De Moivre's Theorem would he what I'd do.
Technically they are not the "cube roots of unity" but simply the "cube roots".
 

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