Question

Argument of the complex number $\left(\frac{-1-3i}{2+i}\right)$is

• A. 45°
• B. 135°
• C. 225°
• D. 240°

Answer 1

Answer: (C)

We have,
$\frac{-1-3i}{2+i}=\frac{-1-3i}{2+i}\times \frac{2-i}{2-i}=\frac{-2-5i+3i^2}{4-i^2}$
$=-1-i$
Now, let us put -1 = r cos$\theta ,-1=rsin\theta$
Squaring and adding, r${}^2$ = 2 i.e., r =$\sqrt{2}$
So that cos $\theta =\frac{-1}{\sqrt{2}},sin\theta =\frac{-1}{\sqrt{2}}$
Therefore,$\theta =225°$
Thus, argument is 225°.