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

1 Answer
Shiva Prakash M V
Jul 26, 2018

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

Explanation:

#(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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