1. ## HorribleArgand Diagram Question

Hey,
i have a question.

"the roots of a certain equation, when plotted on an argand diagram, represent the vertices of a square. one vertex has a modulus of 2 and an argument of PI/3 (3.1415/3).

Find the original equation and the three remaining vertices."

Any help would be much appreciated,
Ned

2. Originally Posted by Ned Hunter
Hey,
i have a question.

"the roots of a certain equation, when plotted on an argand diagram, represent the vertices of a square. one vertex has a modulus of 2 and an argument of PI/3 (3.1415/3).

Find the original equation and the three remaining vertices."

Any help would be much appreciated,
Ned
note that if you have a complex number $\displaystyle \, z = w^n \,$ and you want to find all its n roots, then

$\displaystyle w_k = r^{\frac{1}{n}} \, cis (\frac{\theta + 2k\pi}{n})$
where k=0,1,...,n-1

you can use this fact to find what you want..

3. thank you. i actually worked it out about 5 minutes after i posted, using that formula that i had already, i was just getting stuck fiddling around with the 2pik

Cheers