[<< wikibooks] Circuit Theory/Phasors/proof2
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    {\displaystyle g(t)=G_{m}sin(\omega t)}
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    {\displaystyle g(t)=G_{m}cos(\omega t-{\frac {\pi }{2}})}
  

  
    
      
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    {\displaystyle g(t)=G_{m}\operatorname {Re} (e^{j(\omega t-{\frac {\pi }{2}})})}
  

  
    
      
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    {\displaystyle g(t)=G_{m}\operatorname {Re} (e^{-j*{\frac {\pi }{2}}}e^{j\omega t})}
  

  
    
      
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    {\displaystyle g(t)=\operatorname {Re} (G_{m}e^{-j*{\frac {\pi }{2}}}e^{j\omega t})}
  

  
    
      
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    {\displaystyle g(t)=\operatorname {Re} (\mathbb {G} e^{j\omega t})}
  

  
    
      
        
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    {\displaystyle \mathbb {G} =G_{m}e^{-j*{\frac {\pi }{2}}}=G_{m}(cos(-{\frac {\pi }{2}})+j*sin(-{\frac {\pi }{2}}))=-jGm}