Concept:The argument of a complex number z=x+iy is θ=tan−1(y/x), adjusted for the quadrant where z lies.Explanation:Given z=−3+i2(1+2i).Multiply numerator and denominator by the conjugate of the denominator: (3−i).z=−3+i2(1+2i)×3−i3−i.Simplify numerator: (1+2i)(3−i)=3+6i−i−2i2=3+5i+2=5+5i.So numerator becomes 2(5+5i)=10+10i.Denominator: (3+i)(3−i)=9−i2=9+1=10.Thus z=−1010+10i=−(1+i)=−1−i.Here x=−1, y=−1, both negative, so z lies in the third quadrant.The principal argument θ (with −π<θ≤π) is given by θ=−π+tan−1(y/x).tan−1(y/x)=tan−1(1)=π/4.Therefore θ=−π+π/4=−3π/4.Answer:−43π, which corresponds to option D.