Eesaasaleem
Eesaasaleem
02-03-2018
Mathematics
contestada
If Z = 2(cos95 - isin95)
Find Z^2
Respuesta :
iGreen
iGreen
02-03-2018
So we have:
[tex]\sf (2(cos(95\textdegree)- i sin(95\textdegree)))^2[/tex]
Convert to radians:
[tex]\sf (2(cos(\dfrac{19}{36}\pi)- i sin(\dfrac{19}{36}\pi)))^2[/tex]
Use the identity: [tex]\sf cos(x)-isin(x)=e^{-ix}[/tex]
[tex]\sf (2e^{-i\frac{19}{36}\pi})^2[/tex]
Simplify:
[tex]\sf e^{-i\frac{19}{36}\pi}=\dfrac{1}{(-1)^{\frac{19}{36}}}[/tex]
[tex]\sf (2\times\dfrac{1}{(-1)^{\frac{19}{36}}})^2\rightarrow \boxed{\sf 4(-1)^{\frac{17}{18}}}[/tex]
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