Asked by Baar
Given that a complex number Z. = 1 + cos 2@ + isin 2@. Calculate its argument
Answers
Answered by
Steve
z = 1+cos2θ + i sin2θ
we want z = r(cosØ+i sinØ), where
cosØ = 1+cos2θ
sinØ = sin2θ
That means that
(1+cos2θ)^2 + sin^2(2θ) = 1
2 + 2cos2θ = 1
cos2θ = -1/2
cosØ = 1 - 1/2 = 1/2
sinØ = √3/2
Ø = π/3
we want z = r(cosØ+i sinØ), where
cosØ = 1+cos2θ
sinØ = sin2θ
That means that
(1+cos2θ)^2 + sin^2(2θ) = 1
2 + 2cos2θ = 1
cos2θ = -1/2
cosØ = 1 - 1/2 = 1/2
sinØ = √3/2
Ø = π/3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.