salam
1) 2i = 2(cospi/2 + i.sinpi/2)
V3 + i = 2(V3/2 + i.1/2) = 2(cospi/6 + i.sinpi/6)
v2(1+i)= 2(V2/2 + i.V2/2) = 2(cospi/4 + i.sinpi/4)
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2)formule de moivre
a^12 = 2^12.(cos12pi/2 + i.sin12pi/2)
= 2^12.cos6pi + i.sin6pi) = 2^12
b^12 = 2^12(cos2pi + i.sin2pi) = 2^12
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c/b= V2(1+i)/(V3 + i) = V2(1+i)(V3-i) /4
= 1/4.[(V6 + V2) + i(V6 - V2)]
c/b=2/2.(cos(pi/4-pi/6) + i.sin(pi/4-pi/6))
= cospi/12 + i.sinpi/12
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cospi/12 = 1/4(V6+V2)
sinpi/12 = 1/4.(V6-V2)
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|a| =|b| = |c| = 2======> OA=OB=OC
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(OB,OC) = arg(c/b) = pi/12 [2pi]
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[z - 2i| = |z-(V3+i)| <===> AM = BM
<===> M € mediatrice [AB].
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