Given, w = 1 $$-$$ $$\sqrt 3 $$ i

$$ \Rightarrow |w| = \sqrt {{{(1)}^2} + {{( - \sqrt 3 )}^2}} = 2$$

Also, given | zw | = 1

$$ \Rightarrow $$ | z | | w | = 1 (using property)

$$ \Rightarrow $$ | z | = $${1 \over 2}$$

Also, arg(z) $$-$$ arg(w) = $${{\pi {} } \over 2}$$

$$ \therefore $$ Angle between two complex number z and w is $${{\pi {} } \over 2}$$.

$$ \therefore $$ $$\angle zow = {{\pi {} } \over 2}$$

$$ \therefore $$ $$\Delta$$zow is a right angle triangle with base $$ow = 2$$ and height $$oz = {1 \over 2}$$

$$ \therefore $$ Area = $${1 \over 2} \times 2 \times {1 \over 2} = {1 \over 2}$$