98/ \(z_2=3-5i\Rightarrow\overline{z}^2=\left(3+5i\right)^2=9+30i-25=30i-16\)
\(\Rightarrow w=\left(2+4i\right)\left(30i-16\right)=60i-32-120-64i=-4i-152\)
=> D
99/ Voi so phuc \(z=x+yi\left(x,y\in R\right)\) duoc bieu dien boi diem \(M\left(x;y\right)\)
\(pt\Leftrightarrow\left(3+2i\right)\left(x+yi\right)+\left(2-i\right)^2-4-i=0\)
\(\Leftrightarrow3x+3yi+2xi-2y+4-4i-1-4-i=0\)
\(\Leftrightarrow3x-2y-1+\left(3y+2x-5\right)i=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-2y-1=0\\3y+2x-5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\Rightarrow M\left(1;1\right)\) =>C
100/ \(pt\Leftrightarrow\left(1-2\sqrt{3}i-3\right)\left(x+yi\right)-4+3i=0\)
\(\Leftrightarrow x+yi-2\sqrt{3}xi+2\sqrt{3}y-3x-3yi-4+3i=0\)
\(\Leftrightarrow-2x+2\sqrt{3}y-4+\left(y-2\sqrt{3}x-3y+3\right)i=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2x+2\sqrt{3}y-4=0\\-2y-2\sqrt{3}x+3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x+2\sqrt{3}y=4\\-2\sqrt{3}y-6x=-3\sqrt{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3\sqrt{3}-4}{8}\\y=\dfrac{4+\dfrac{3\sqrt{3}-4}{4}}{2\sqrt{3}}\end{matrix}\right.\)
\(\Rightarrow Modun=\sqrt{x^2+y^2}=\dfrac{5}{4}\) =>A
P/s: Nhìn chữ Chuyên Hạ Long lại nhớ Quảng Ninh zl :(
