Write each number in complex polar form:
[tex]z=2e^{i\cdot30^\circ}[/tex]
[tex]w=5e^{i\cdot60^\circ}[/tex]
When you multiply two exponential expression with the same base (here, that's e), you end up adding the exponents, so that
[tex]zw=(2\cdot5)e^{i\cdot30^\circ+i\cdot60^\circ}=10e^{i\cdot90^\circ}=10i[/tex]
so the angle of the product zw is 90°.
