Find modulus and argument of \omega=\frac{\sin(P+Q)+i(1-\cos(P+Q))}{(\cos P+\cos Q)+i(\sin P-\sin Q)}

Tessa Leach 2022-01-25 Answered
Find modulus and argument of ω=sin(P+Q)+i(1cos(P+Q))(cosP+cosQ)+i(sinPsinQ)
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Expert Answer

coolbananas03ok
Answered 2022-01-26 Author has 20 answers
We have
N=sin2(P+Q)+(1cos(P+Q))2=sin2(P+Q)+cos2(P+Q)+12cos(P+Q)
=2(1cos(P+Q))=22sin2P+Q2=4sin2P+Q2
and
D=cos2P+cos2Q+sin2P+sin2Q+2(cosPcosQsinPsinQ)
=2+2(cos(P+Q))=2(1+cos(P+Q))=4cos2P+Q2
Now,
|ω|=ND=tanP+Q2
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