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

Tessa Leach

Answered question

2022-01-25

Find modulus and argument of ω=sin(P+Q)+i(1cos(P+Q))(cosP+cosQ)+i(sinPsinQ)

Answer & Explanation

coolbananas03ok

coolbananas03ok

Beginner2022-01-26Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?