If z is a complex number such that z = 2, then the area (in sq. units) of the triangle whose vertices are given by z , - i z and i z - z is equal to

Question

If z is a complex number such that z = 2, then the area (in sq. units) of the triangle whose vertices are given by z , - i z and i z - z is equal to,

MARKS App · Accepted Answer

Let z = x + i y ∴ points will be x , y , y , - x , - x - y , - y + x Area of the triangle for these points as vertices = 3 2 x 2 + y 2 sq. units ∵ z = x 2 + y 2 = 2 ⇒ x 2 + y 2 = 4 ∴ Area of triangle = 6 sq. units

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