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Q.
Let $w =\frac{ z ^2-3 z +6}{ z +1}$ and $z =1+ i ($ where $i =\sqrt{-1})$, then $| w |$ and amp $w$ respectively are
Complex Numbers and Quadratic Equations
Solution:
$w =\frac{(1+ i )^2-3(1+ i )+6}{2+ i }=\frac{3- i }{2+ i }=\frac{(3- i )(2- i )}{5}=\frac{5-5 i }{5}=1- i $
$\text { Hence } | w |=\sqrt{2} \text { and amp. } w =-\frac{\pi}{4} $