Mathematics - Complex Number Question with Solution | TestHub

$z_0=w$or$w^2$

When$z_0=w$

$z=3+6i\times w^{81}-3i\times w^{93}$

$=3+6i-3i=3+3i$

When$z_0=w^2$

$z=3+6i\times {\left(w^2\right)}^{81}-3i\times {\left(w^2\right)}^{93}$

$=3+6i-3i=3+3i$

$\therefore \arg \left(z\right)={\tan }^{-1}\left(\frac{Im\left(z\right)}{Re\left(z\right)}\right)={\tan }^{-1}\left(\frac{3}{3}\right)=\frac{\pi }{4}$