Question

Argument of $\frac {1-i√3}{1+i√3}$ is

• A. 60°
• B. 210°
• C. 120°
• D. 240°

Answer 1

Answer: (D)

240°

Answer 2

Let z = $\frac {1−i \sqrt{3}}{1+i \sqrt{3}}$
z = $\frac {1−i \sqrt{3}}{1+i \sqrt{3}}$ ​ x $\frac {1−i \sqrt{3}}{1-i \sqrt{3}}$
z = $\frac {(1−i \sqrt{3})^2}{1+3}$
z = $\frac {-2−2i \sqrt{3}}{4}$
z = $-\frac {1}{2} - \frac {i\sqrt {3}}{2}$
Now r = $\sqrt {(-\frac {1}{2})^2 + (-\frac {\sqrt{3}}{2})^2 }$
r = 1
On comparing with z = r cos α + ir sin α
r cos α=​ $-\frac {1}{2}$
cos α =​ $-\frac {1}{2}$
cos α = cos 240o
α = 240o
Therefore the correct option is (D) 240o