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  • A pen moving with velocity on the page according to the given relation - <img alt="V(\theta)=\cos \theta+i \sin \theta" src="/latex-image/?V%28%5Ctheta%29%3D%5Ccos%20%5Ctheta&plus;i%2

A pen moving with velocity on the page according to the given relation -

V(\theta)=\cos \theta+i \sin \theta, where i is complex number . Acceleration is proportional to-

 

Option: 1

\mathrm{i e^\theta}


Option: 2

\mathrm{i e^{i \theta}}


Option: 3

\mathrm{\frac{1}{2} i e^0}


Option: 4

\mathrm{\frac{1}{2} i e^{i o}}


Answers (1)

best_answer

velocity V(\theta)=\cos \theta+i \sin \theta -----------(1)

Acceleration \frac{d v(\theta)}{d t}=\frac{d}{d t}[\cos \theta+i \sin \theta]

but we know that \cos \theta+i \sin \theta=e^{i \theta} then acceleration equation will become-

\begin{aligned} \frac{d v(\theta)}{d t}=\frac{d}{d t} e^{i \theta} & \Rightarrow e^{i \theta} \frac{d}{d t}(i \theta) \\ & \Rightarrow e^{i \theta} \cdot i \\ & \Rightarrow i e^{i \theta} \text { Ans. } \end{aligned}

Posted by

Pankaj

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