Complex Numbers Question

Just work out the arg of each. When are the arg multiples equal (lowest common multiple) as they have unit modulus. Should be 3-4 simple lines?

That's what I tried to do above - unless you mean keeping them in complex number form rather than converting to mod-arg form?

If so I'm not sure how to find the arg when it's raised to a variable? Without expanding via binomial but then it'll get messy?

(e^(it))^n = e^(int)
So an angle t raised to the power n is nt. Multiple angles are actually useful. Think of it as a rotation by t applied n times.
So yes, it's what you did, but easier to work directly on
nt = mu + 2kpi
for args t,u, rather than putting in rectangular cis form.

The exponential power-multiple angle is basically demoivres theorem, but easy to get using basic exponent rules.

The argument can be [0,2pi] or [-pi,pi]
But you're looking for .
m(5pi/6) - n(pi/4) = k2pi
Clearly n is a multiple of 3 and you could take k=0 to keep things easier.

Sorry I'm lost - not sure why the arg = 5pi/6 ? And where the k2pi is from?

Had a go at the below question but ended up with a pair of sim equations that don't solve - does anyone know if I've made an error or if there's a better approach to this?