Question

If $arg\left(z_1\right)={170}^o$ and $arg\left(z_2\right)={70}^o$, then find the principle argument of $z_1{z}_2$.

• A. ${240}^o$
• B. ${120}^o$
• C. $-{120}^o$
• D. $-{240}^o$

Answer 1

The correct option is C $-{120}^o$

$z_1=|z_1|e^{i\left({170}^0\right)}$
$z_2=|z_2|e^{i\left({70}^0\right)}$
Then
$z_1.z_2=|z_1|z_2|.e^{i\left(240\right)}$
$=|z_1|z_2|.e^{i\left(240\right)}$
Now ${240}^0$ is in third quadrant. Hence, the principle argument will be
$-({180}^0-{60}^0)$
$=-{120}^0$