Q1) Prove that for any two complex numbers $\displaystyle z_{1}$ and $\displaystyle z_{2}$ , $\displaystyle |\frac{z_{1}}{z_{2}}| = \frac{|z_{1}|}{|z_{2}|}$. Is it true to write Arg$\displaystyle (z_{1}z_{2})=$ Arg$\displaystyle (z_{1})$$\displaystyle +$ Arg$\displaystyle (z_{2})$. Support your ideas geometrically.

Q2) Show that $\displaystyle z^{\frac{1}{n}}$ has $\displaystyle n$ distinct values for natural number $\displaystyle n$. What can you say about non-natural values of $\displaystyle n$? Why?

For question 1, i know that, if one the argument is negative, that equation isn't true because of essential argument thing but i don't know how to explain it at exam paper and how to support it geometrically.

For question 2, i didn't understand a thing. so don't know where to begin solving.