Question

Find the modulus, argument and the principal argument of the complex numbers.
$\frac{2+i}{4i+(1+i{)}^2}$

Answer 1

$=\frac{2+i}{4i+(1+i)2}$

$\Rightarrow \frac{2+i}{4i+1-1+2i}$

$\frac{2+i}{6i}$

$\frac{1}{3i}+\frac{1}{6}$

$\frac{1}{6}-\frac{i}{3}$

$z=\frac{1}{6}-\frac{i}{3}$

$|z|=\sqrt{\frac{1}{36}+\frac{1}{9}}=\frac{\sqrt{5}}{6}$

principal Arg(2)= $\pi ta{n}^{-1}\left(\frac{-V_3}{V6}\right)$$\pi ta{n}^{-1}(-2)$

$=\pi -ta{n}^{-1}\left(2\right)$

$=\pi -63.44$

and arg(2)$=2K\pi +\pi -63.44$

$=2(K+1)\pi -63.44$