Question

Which of the following is correct for any two complex numbers $z_{1}$ and $z_{2}$ ?

• A. $|z_{1} z_{2}|=|z_{1}| |z_{2}|$
• B. arg $(z_{1}z_{2}) = arg (z_{1}) \cdot arg (z_{2})$
• C. $|z_{1}+z_{2}|=|z_{1}|+|z_{2}|$
• D. $|z_{1}+z{2}| \ge |z_{1}|-|z_{2}|$

Answer 1

Answer: (A)

$|z_{1} z_{2}|=|z_{1}| |z_{2}|$

Answer 2

$\left(a\right)$ $\left|z_{1}z_{2}\right|=\left|z_{1}\right|\left|z_{2}\right|$ $\left(b\right)$ arg $\left(z_{1}z_{2}\right) = arg \left(z_{1}\right) + arg \left(z_{2}\right)$ $\left(c\right)$ $\left|z_{1}+z_{2}\right|\ne\left|z_{1}\right|+\left|z_{2}\right|$ $\left(d\right)$ $\left|z_{1}+z_{2}\right|\le\left|z_{1}\right|-\left|z_{2}\right|$