We are given z1⋅z2=0. If z2=0 then there is nothing more to prove.
So suppose that z2=0, then from the field properties of real numbers z21 the multiplicative inverse exists.
And
\(\displaystyle \begin{array}{l}
0 = z_1 z_2 \\
0\left( {\frac{1}{{z_2 }}} \right) = z_1 z_2 \left( {\frac{1}{{z_2 }}} \right) \\
0 = z_1 \\
\end{array}\),
we are done.
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