Finding Modulus and Argument for Complex Number $z$ Assume the Complex Number $z$ has argument $$\pi $$ and modulus $$\sqrt{3} $$ how would i find argument and modulus for $$-2iz$$ i already know the correct answer for this(it's from an old test) but i don't know how its calculated. I know how to find modulus and argument but im not sure about this exact math problem. Any help is greatly appreciated, please tell me if i should provide more info.

Since we have the modulus and argument, we know that $z=-\sqrt3$, hence we get $-2iz=2\sqrt3i$.  The argument and modulus for that complex number are $\pi/2$ and $2\sqrt3$.
For explanation, the key is Euler's formula:  $e^{i\theta}=\cos\theta+i\sin\theta$.  This allows us to identify every point $z=x+iy$ in the complex plane with a pair $(r,\theta)$, via $z=re^{i\theta}$..
