Which of the following is correct for any two complex numbers z1 and z2 -a z 1 z 2- z 1 z 2b argz 1 z 2- z 1 argz 2c z 1- z 2- z 1- z 2d z 1- z 2 - z 1- z 2

Since, it is known that z1z2=z1z2, argz1z2=argz1+argz2 nbsp;and z1+z2 #8804;z1+z2 Hence, the correct option is (a). ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Which of the ...

Question

Which of the following is correct for any two complex numbers z₁ and z₂?

(a) $|z_{1} z_{2}| = |z_{1}| |z_{2}|$
(b) $\arg (z_{1} z_{2}) = \arg (z_{1}) \arg (z_{2})$
(c) $|z_{1} + z_{2}| = |z_{1}| + |z_{2}|$
(d) $|z_{1} + z_{2}| \geq |z_{1}| + |z_{2}|$

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Solution

Since, it is known that
$|z_{1} z_{2}| = |z_{1}| |z_{2}|$ ,
$\arg (z_{1} z_{2}) = \arg (z_{1}) + \arg (z_{2})$ and
$|z_{1} + z_{2}| \leq |z_{1}| + |z_{2}|$

Hence, the correct option is (a).

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