Question

帮忙解决一下数学题么

帮忙解决一下数学题么非常感谢帮忙

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Answer 1

(1+itan30)^6=(1+i/√3)^6=(√3+i)^6/(√3)^6=(2+2√3i)^3/3^3=2^3(1+√3i)^3/3^3
=2^3(-2+2√3i)(1+√3i)/3^3=-2^4(1-√3i)(1+√3i)/3^3=-2^4*4/27=-64/27
(cos75+isin75)(sin75+icos75)/i^103
=[cos75sin75+i(sin75sin75+cos75cos75)+icos75sin75]/[(i^4)^25*i^3]
=[cos75sin75+i+icos75sin75]/i^3
=icos75sin75-1-cos75sin75
=-1-sin150/2+isin150/2
=-1-sin30/2+isin30/2
=-5/4+i/4
-i/(cos150-isin150)=-i/(-cos30-isin30)=-i/(-√3/2-i/2)=2i/(√3+i)=2i(√3-i)/2=1+√3i