Question

Find the modulus, argument and the principal argument of the complex numbers.
$6(\cos {310}^o-i\sin {310}^o)$

Answer 1

For $z=r\left(\cos \right(\theta )+i\sin (\theta \left)\right)$
$|z|=|r|$
$\arg \left(z\right)=\theta$
Principal argument is the argument that is in the interval $(-{180}^o,{180}^o]$
Here,
$|z|=6$
Argument = $-{310}^o$
Principal argument = $-{310}^o+{360}^o={50}^o$