<prompt> Ikiwa z ni nambari changamano kama hiyo z z-1 sqrt3,thamani ya nini z2010 z-2010 , ?  <response>: Tunaanza kwa kujaribu kueleza z kwa njia inayofaa zaidi.Tumepewa kuwa z z-1 sqrt3 frac2sqrt32 2 cosfracpi6Kwa hivyo tunajua kuwa z ni textcisfracpi6 au textcis-fracpi6Sema kwamba z textcisfracpi6. Kisha,z2010 lefttextcisfracpi6right2010 textcisfrac2010pi6 textcis335pi textcispi -1.Kisha z-1 -1-1 -1. Hivyoz2010 z-2010 -1 -1 -2.Vile vile, ikiwa z textcis-fracpi6 . Kisha,z2010 lefttextcis-fracpi6right2010 textcis-frac2010pi 6 textcis-335pi textcis-pi -1.Kisha z-1 -1-1 -1. Hivyoz2010 z-2010 -1 -1 -2. 