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Question
Which of the following is correct for any two complex numbers z1 and z2?
Options
\[\left| z_1 z_2 \right| = \left| z_1 \right|\left| z_2 \right|\]
\[\arg\left( z_1 z_2 \right) = \arg\left( z_1 \right) \arg\left( z_2 \right)\]
\[\left| z_1 + z_2 \right| = \left| z_1 \right| + \left| z_2 \right|\]
\[\left| z_1 + z_2 \right| \geq \left| z_1 \right| + \left| z_2 \right|\]
Solution
Since, it is known that
\[\left| z_1 z_2 \right| = \left| z_1 \right|\left| z_2 \right|\]
\[\arg\left( z_1 z_2 \right) = \arg\left( z_1 \right) + \arg\left( z_2 \right)\] and
\[\left| z_1 + z_2 \right| \leq \left| z_1 \right| + \left| z_2 \right|\]
Hence, the correct option is (a).
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