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Question Number 29522 by 803jaideep@gmail.com last updated on 09/Feb/18

Commented by 803jaideep@gmail.com last updated on 09/Feb/18

$$40\mathrm{th}\mathrm{ques}\mathrm{sry}$$

Commented by Tinkutara last updated on 09/Feb/18

120?

Commented by 803jaideep@gmail.com last updated on 09/Feb/18

$$\mathrm{yes}\mathrm{yes}\mathrm{but}\mathrm{how}$$

Commented by Tinkutara last updated on 09/Feb/18

See Q 20739

Commented by math solver last updated on 10/Feb/18

$$istheans.ofq.39A?$$

Commented by prof Abdo imad last updated on 11/Feb/18

$$38)ifz=cos\alpha +isin\alpha letfindarg(z^2+z^{-})$$$$themoivreformulagive{z}^2=cos\left(2\alpha \right)+isin\left(2\alpha \right)$$$$amd{z}^{-}=cos\alpha -isin\alpha \Rightarrow$$$$z^2+z^{-}=cos\alpha +cos\left(2\alpha \right)+i(sin\left(2\alpha \right)-sin\alpha )$$$$=2cos\left(\frac{3\alpha }{2}\right)cos\left(\frac{\alpha }{2}\right)+i(sin\left(2\alpha \right)-sin\alpha )$$$$sinp?-sinq=cos(\frac{\pi }{2}-p)+cos(\frac{\pi }{2}+q)$$$$=2cos\left(\frac{\pi -p+q}{2}\right)cos\frac{p+q}{2}=2sin\left(\frac{p-q}{2}\right)cos\left(\frac{p+q}{2}\right)$$$$sin\left(2\alpha \right)-sin\alpha =2sin\left(\frac{\alpha }{2}\right)cos\left(\frac{3\alpha }{2}\right)\Rightarrow$$$$z^2+z^{-}=2cos\left(\frac{3\alpha }{2}\right)(cos\left(\frac{\alpha }{2}\right)+isin\left(\frac{\alpha }{2}\right)\Rightarrow$$$$arg(z^2+z^{-})=\frac{\alpha }{2}.$$

Commented by math solver last updated on 11/Feb/18

$$\mathrm{wow},\mathrm{sir}.$$

Answered by 803jaideep@gmail.com last updated on 09/Feb/18

$$10\mathrm{th}$$

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