Complex numbers loci

The complex number 1+2i is denoted by u. The complex number v is such that |v|= 2|u| and arg v =arg u+ pi/3.
Sketch on Argand diagram showing the points representing u and v.
So i plotted u=(1,2) in the first quadrant and v=(-2.5,3.8) in the second quadrant.
Is this correct?

I got 3.7 (2sig.fig.) for the second coordinate, but it only asks for a sketch, so that's fine.

Edit: I'd mark in the angle pi/3, and the length $2\sqrt 5$ for good measure.

Thanks a lottt! Can you also pls help me with one more question.
Its the continuation of the same question. I got w=1/2+(sqroot 3)/2 i
How do i explain why v can be expressed a 2uw?

Consider the different ways to represent complex numbers, and think about how you get to v from u, in particular at the very start of the question.

Consider the different ways to represent complex numbers, and think about how you get to v from u, in particular at the very start of the question.

Consider the different ways to represent complex numbers, and think about how you get to v from u, in particular at the very start of the question.

So v= -2.5+ 3.7 i

Doesn't the question ask for exact values for a and b, i.e. you leave the square roots (surds) in the answer?

Thank you so much.
But the ans in the mark scheme is correct of what I have mentioned.