Complex numbers question! (Roots of equation)

The question is 15iii on here: http://www.dur.ac.uk/c.c.d.s.caiado/wbook2012.pdf

"Use part ii to find the three distinct roots of the equation

z^3=1

. Draw them on the complex plane and convert them from modulus-argument form to real-imaginary form."

In part ii I showed that

re^ (i\theta)

=1 (for real theta and r>0) if and only if r=1 and theta=2.n.pi for some integer n..

Thanks, any ideas would be much appreciated! (+rep)

(edited 11 years ago)

You know we can write any z in the form

r e^{i\theta}

. So if

z = r e^{i\theta}

, what is z^3? Now use part (ii)

What can you do with an arts degree?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like