Let a complex number be w = 1 - 3 i . Let another complex number z be such that | z w | = 1 and arg z - arg w = π 2 . Then the area of the triangle (in sq. units) with vertices origin, z and w is equal to

Question

Let a complex number be w = 1 - 3 i . Let another complex number z be such that | z w | = 1 and arg z - arg w = &#960; 2 . Then the area of the triangle (in sq. units) with vertices origin, z and w is equal to

Aicharya · Accepted Answer

w = 1 - 3 i &#8658; | w | = 2 Now, z = 1 | w | &#8658; z = 1 2 and amp z = &#960; 2 + amp w &#8658; Area of triangle = 1 2 . OP . OQ = 1 2 &#183; 2 &#183; 1 2 = 1 2 Sq. units

Let a complex number be w = 1 - 3 i . Let another complex number z be such that | z w | = 1 and arg z - arg…

Solution