Answer:
2pi/3
Step-by-step explanation:
Given are two complex numbers as
[tex]z1=6(cos\frac{3\pi }{2} +isin\frac{3\pi }{2}) \\z2=[tex]
We are to find the argument of z1/z2
Since both are in mod, argument form we can use Demoivre theorem for complex numbers to find the quotient
Quotient =
[tex]\frac{z1}{z2} =\frac{6(cos\frac{3\pi }{2} +isin\frac{3\pi }{2})}{2(cos\frac{5\pi }{6} +isin\frac{5\pi }{6})} \\=\frac{6}{2} (2(cos\frac{4\pi }{6} +isin\frac{4\pi }{6})\\=3 (cos\frac{2\pi }{3} +isin\frac{2\pi }{3})[/tex]
Thus we find that argument = 2pi/3
