Çözüldü Coordinate Geometry - Principal Argument of Complex Numbers

In an ABCO parallelogram situated on the complex plane with O as the origin, if the complex numbers corresponding to points A and C are 3 + i and 1 + 3i, respectively, what is the principal argument of the complex number representing point B?

A) -π / 4
B) -π / 3
C) π / 4
D) π / 2
E) 2π / 3

The coordinates of the vertices A and C are A(3, 1) and C(1, 3).
Equation of the side [AO]: y = x / 3
Equation of the side [BC]: y - 3 = (1 / 3)(x - 1) ⇒ y = 3 + (1 / 3)(x - 1)....(I)
Equation of the side [CO]: y = 3x
Equation of the side [AB]: y - 1 = 3(x - 3) ⇒ y = 1 + 3(x - 3)....(II)
Intercepting the lines (I) and (II) the one-variable equation 3 + (1 / 3)(x - 1) = 1 + 3(x - 3) yields the abscissa of the point B as x = 4,
Substituting 4 for the equations I (or II), the ordinate of the point B is y = 3 + (1 / 3)(4 - 1) = 3 + 1 = 4.
Since the real and imaginary numbers of the point B are the same, 4 and 4, the complex number at that point is 4 + 4·i, so;
Arg(4 + 4·i) = arctan(4 / 4) = π / 4.

Source (Turkish): "LYS Matematik Soru Bankası", Karekök Press, 7th Edition, September 2012, Page 301, Question 18