Răspuns:
Explicație pas cu pas:
Facem transformările: cos220°=cos(180°+40°)=-cos40°,
sin220°=sin(180°+40°)=-sin40°. La următoarele transformări, se aplică formulele: cosα·cosβ-sinα·sinβ=cos(α+β); sinα·cosβ+sinβ·cosα=sin(α+β).
b) [4·(cos220°+i·sin220°)]·[1,5·(cos20°+i·sin20°)]=[4·(-cos40°-i·sin40°)]· [1,5·(cos20°+i·sin20°)]=-6·[(cos40°+isin40°)(cos20°+isin20°)]=-6·[cos40°·cos20°+i·cos40°·sin20°+i·sin40°·cos20°+i²·sin40°·sin20°]=-6·[(cos40°·cos20°-sin40°·sin20°)+i·(cos40°·sin20°+sin40°·cos20°)]=-6·[cos(40°+20°)+i·sin(40°+20°)]=-6·[cos60°+i·sin60°]= -6·[(1/2)+i·(√3/2)]=-3-i·3√3.
