Let O be the origin, the point A be z₁= 3 +2 2 i , the point B (z₂ ) be such that 3 |z₂ |= |z₁ | and (z₂ )= (z₁ )+ 6 . Then

Step-by-step solution

aligned & O A= |z₁ |= 3+8 = 11 & and O B= 1 3 |z₁ |= 11 3 & A B^2=O A^2+O B^2-2 O A O B 6 & =11+ 11 3 -2 11 3 3 2 & A B= 11 3 & Area of A B D= 1 2 O A O B 6 & = 11 4 3 sq. units aligned Here O B=A B and A= 2 3 A B D is an obtuse angled isosceles triangle.