Prove that if $z_1*z_2=0$ then at least one of $z_1$ and $z_2$ must be 0. $z_1$ and $z_2$ are complex numbers by using the following property: $|z_1z_2|=|z_1||z_2|$
if $z_1*z_2=0$ then $$|z_1*z_2|=|0|$$ $$|z_1*z_2|=0$$ $$|z_1||z_2|=0$$
This implies that at least one $z_i$ must be 0 so $|z_i|=0$
How does that look?