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Last Problem I promise

 

Multiply (2.89cis 62.31\deg)(11cis 102.05\deg )

 

Thanks again smiley

 Jun 13, 2022
 #1
avatar+579 
+2

\((2.89 (\cos(62.31 °) + i \sin(62.31 °))) (11 (\cos(102.05 °) + i \sin(102.05 °)))\)

 

Converting to rad:

 

\(\frac{289}{100}\left(\cos \left(\frac{2077\pi }{6000}\right)+i\sin \left(\frac{2077\pi }{6000}\right)\right)\cdot \:11\left(\cos \left(\frac{2041\pi }{3600}\right)+i\sin \left(\frac{2041\pi }{3600}\right)\right)\)

 

\(\mathrm{Use\:the\:Euler's\:formula}:\quad \cos \left(x\right)+i\sin \left(x\right)=e^{ix}\)

 

\(\frac{289}{100}\left(\cos \left(\frac{2077\pi }{6000}\right)+i\sin \left(\frac{2077\pi }{6000}\right)\right)11\left(\cos \left(\frac{2041\pi }{3600}\right)+i\sin \left(\frac{2041\pi }{3600}\right)\right)=11\frac{289}{100}e^{i\frac{2041\pi }{3600}}e^{i\frac{2077\pi }{6000}}\)

 

\(11\cdot \frac{289}{100}e^{i\frac{2041\pi }{3600}}e^{i\frac{2077\pi }{6000}}\)

 

\(\frac{3179\left(-1\right)^{\frac{4109}{4500}}}{100}\)

 

-Vinculum

 Jun 13, 2022

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