Question

$$\begin{array}{cc}\underset{–}{ComplexNumber}& \underset{–}{PrincipalArgument\left(inradians\right)}\\ 1)1+i& a)\frac{3\pi }{4}\\ 2)1-i& b)\frac{\pi }{4}\\ 3)-1+i& c)\frac{-3\pi }{4}\\ 4)-l-i& d)\frac{-\pi }{4}\end{array}$$

• A. 1 →a, 2 →b, 3 →c, 4 →d
• B. 1 →b, 2 →a, 3 →c, 4 →d
• C. 1 →b, 2 →d, 3 →a, 4 →c
• D. 1 →d, 2 →a, 3 →b, 4 →c

Answer 1

The correct option is C

1 →b, 2 →d, 3 →a, 4 →c

1) 1 + i $\equiv$ (1,1) is in $1^{st}$ quadrant

$\alpha ={\tan }^{-1}|\frac{1}{1}|=\frac{\Pi }{4}$

$\theta =\alpha =\frac{\Pi }{4}$

2) 1 + i $\equiv$ (1,-1) is in $4^{th}$ quadrant

$\alpha ={\tan }^{-1}|\frac{-1}{1}|=\frac{\Pi }{4}$

$\theta =-\alpha =\frac{-\Pi }{4}$

3) -1 + i $\equiv$ (-1,1) is in $2^{nd}$ quadrant

$\alpha ={\tan }^{-1}|\frac{1}{-1}|=\frac{\Pi }{4}$

$\theta =\Pi -\alpha =\frac{3\Pi }{4}$

4) -2 - 2i $\equiv$ (-2,-2) is in $3^{rd}$ quadrant

$\alpha ={\tan }^{-1}|\frac{-2}{-2}|=\frac{\Pi }{4}$

$\theta =-(\Pi -\alpha )=\frac{-3\Pi }{4}$