VITEEE 2014 Paper

Let z = x + iy, then
z + iz = x + iy + i (x+ iy) = (x-y) + i (x + y) and iz = i (x + iy) = -y + ix,
Then, the area of the triangle formed by these lines is
Δ =

1

2

|

x	y	1
(x−y)	(x+y)	1
−y	x	1

|
Applying R2 → R2 - (R1+R3)
Δ =

1

2

|

x	y	1
0	0	−1
−y	x	1

| =

1

2

(x2+y2)
⇒

1

2

|z|2 = 200 (given)
|z|2 = 400 ⇒ |z| = 20
∴ 3 |z| = 3 × 20 = 60