Toán 12 [TÓAN 12] Số phức!!!!!!!

I

iloveg8

1/ Tính tổng:
[tex] Q=(1+cos (\frac{ \pi}{4}) +i sin( \frac{ \pi}{4}))^{2009} [/tex]

[TEX]Q = ( cos0 + i sin0 + cos (\frac{ \pi}{4}) +i sin( \frac{ \pi}{4}))^{2009} = [ 2cos(\frac{\pi}{8}) ( cos (\frac{\pi}{8}) +i sin( \frac{ \pi}{8}) ] ^{2009}[/TEX]

[TEX]= ( 2.cos (\frac{\pi}{8})) ^{2009} .( cos (\frac{2009\pi}{8}) +i sin( \frac{2009 \pi}{8}))[/TEX]

2/ [tex] (1+itan A)(1+itanB)(1+itanC) = 1 - ( tanA.tanC + tanA.tanB + tanB.tanC)[/tex]
 
Last edited by a moderator:
C

caothuyt2

2/(1+i.tan A)(1+i.tanB).(1+i.tanC)
=1-tanA.tanB-tanB.tanC-tanA.tanC +i.(tanA+tanB+tanC) -i.tanA.tanB.tanC
=1-tanA.tanB -tanB.tanC-tanA.tanC => đpcm
 
You must log in or register to reply here.
Top Bottom