Complex number - roots (1 Viewer)

[Cujo10]

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

 

[shashysha]

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]

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]

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".