Question

If z1 = 6(cos 3pi/2 + isin 3pi/2) and z2 = 2(cos 5pi/6 + isin 5pi/6), then the argument of z1/z2=

Answer 1

Answer:

2pi/3

Step-by-step explanation:

Given are two complex numbers as

$z1=6(cos\frac{3\pi }{2} +isin\frac{3\pi }{2}) \\z2=[tex]We are to find the argument of z1/z2Since both are in mod, argument form we can use Demoivre theorem for complex numbers to find the quotientQuotient = [tex]\frac{z1}{z2} =\frac{6(cos\frac{3\pi }{2} +isin\frac{3\pi }{2})}{2(cos\frac{5\pi }{6} +isin\frac{5\pi }{6})} \\=\frac{6}{2} (2(cos\frac{4\pi }{6} +isin\frac{4\pi }{6})\\=3 (cos\frac{2\pi }{3} +isin\frac{2\pi }{3})$

Thus we find that argument = 2pi/3

Answer 2

Answer:

2pi/3

Step-by-step explanation:

I had this same exact question and i got that as the answer.