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Can you find [ (2(cos80˚+isin80˚))^3 ] ? then express the answer in rectangular form.

Answer 1

#(2((cos80^0+isin80^0))^3=-4-4isqrt3#

#(2((cos80^0+isin80^0))^3=2^3(cos80^0+isin80^0)^3# By De-Moivre's theorem; #(cosA+isinA)^n=cosnA+isinnA# #=8(cos(3xx80^0)+isin(3xx80^0))# #=8(cos240^0+isin240^0)# 240=180+60 #cos240^0=cos(180^0+60^0)# #=-cos60^0=-1/2# #sin240^0=sin(180^0+60^0)# #=-sin60^0=-sqrt3/2# Thus, #8(cos240^0+isin240^0)=8xx(-1/2+i(-sqrt3)/2)# #=-4-4isqrt3#

#(2((cos80^0+isin80^0))^3=-4-4isqrt3#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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