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Question Number 176049 by doline last updated on 11/Sep/22

calculer (−1/2+i(√(3/2)^3 ))

calculer(−1/2+i3/2)3

Answered by Rasheed.Sindhi last updated on 11/Sep/22

−1/2+i(√(3/2)^3 )) =−(1/2)+i((√(3/2)) )^3 =−(1/2)+i((√(3/2)) )^2 ((√(3/2)) ) =−(1/2)+((3i)/2)∙(((√3) )/( (√2) ))∙(((√2) )/( (√2) )) =−(1/2)+((3i)/2)∙(((√6) )/( 2 )) =−(1/2)+((3i(√6) )/( 4 ))=((−2+3i(√6) )/4)

−1/2+i3/2)3=−12+i(3/2)3=−12+i(3/2)2(3/2)=−12+3i2⋅32⋅22=−12+3i2⋅62=−12+3i64=−2+3i64

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