given that z=5-7i and w=2<-pi/3
1)State Im(z)
2)arg(w)
3)Modulo of w
4)convert z to polar form and w to cartesain form
5) calculate z-w
zw
z/w
Well then you need to write it as $\displaystyle \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right), 2\,\textrm{cis}\,\frac{\pi}{3} \end{align*}$ or $\displaystyle \displaystyle \begin{align*} 2e^{i\frac{\pi}{3}} \end{align*}$.
Anyway, what have you gotten so far?
7 is incorrect. It's actually -7.
As for part 2 and 3, the "modulus" of a complex number is its size or length. How long is $\displaystyle \displaystyle \begin{align*} 2\left(\cos{\frac{\pi}{3}} + i\sin{\frac{\pi}{3}}\right) \end{align*}$? The "argument" is the angle made. What is the angle in this complex number?