[tex]z=5-5i=5(1-i)=5\sqrt2e^{-i\pi/4}[/tex]
[tex]w=\sqrt3-i=2\left(\dfrac{\sqrt3}2-\dfrac12i\right)=2e^{-i\pi/6}[/tex]
[tex]\implies\dfrac zw=\dfrac{5\sqrt2e^{-i\pi/4}}{2e^{-i\pi/6}}=\dfrac5{\sqrt2}e^{-i\pi/12}[/tex]
[tex]\implies\dfrac zw=\dfrac{5+5\sqrt3}4-\dfrac{5\sqrt3-5}4i[/tex]
[tex]\implies zw=10\sqrt2e^{-i5\pi/12}=5\sqrt3-5-(5+5\sqrt3)i[/tex]
