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

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

asked
User Adrian Kosmaczewski
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2 Answers

2 votes

Answer:

2pi/3

Explanation:

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

answered
User Sebastian S
by
8.0k points
5 votes

Answer:

2pi/3

Explanation:

Given are two complex numbers as


z1=6(cos(3\pi )/(2) +isin(3\pi )/(2)) \\z2=[tex]</p><p>We are to find the argument of z1/z2</p><p>Since both are in mod, argument form we can use Demoivre theorem for complex numbers to find the quotient</p><p>Quotient = </p><p>[tex](z1)/(z2) =(6(cos(3\pi )/(2) +isin(3\pi )/(2)))/(2(cos(5\pi )/(6) +isin(5\pi )/(6))) \\=(6)/(2) (2(cos(4\pi )/(6) +isin(4\pi )/(6))\\=3 (cos(2\pi )/(3) +isin(2\pi )/(3))

Thus we find that argument = 2pi/3

answered
User Tetsuo
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