把与复数3-√3i对应的向量旋转60度,得到一个新向量,求新向量对应的复数
\u590d\u53d8\u51fd\u6570\uff1a\u4e00\u5411\u91cf\u987a\u65f6\u9488\u65cb\u8f6c\u220f/3\uff0c\u5411\u53f3\u5e73\u79fb3\u4e2a\u5355\u4f4d\uff0c\u518d\u5411\u4e0b\u5e73\u79fb1\u4e2a\u5355\u4f4d\u540e\u5bf9\u5e94\u7684\u590d\u6570\u4e3a1-\u221a3i\uff0c\u5219\u539f\u5411\u91cf\u5bf9\u9009 A \u3002
\u5411\u91cf\u5728\u5e73\u79fb\u7684\u8fc7\u7a0b\u4e2d\u6240\u4ee3\u8868\u7684\u590d\u6570\u662f\u4e0d\u53d8\u7684\uff0c\u53ea\u6709\u5728\u65cb\u8f6c\u65f6\u624d\u6709\u6240\u53d8\u5316\u3002
\u539f\u5411\u91cf=(1-\u221a3*i)*[cos(\u03c0/3)+i*sin(\u03c0/3)]=(1-\u221a3*i)(1/2+\u221a3/2*i)=2 \u3002
\u5b9e\u9645\u610f\u4e49
\u51fd\u6570\u5e73\u79fb\u7684\u5b9e\u9645\u610f\u4e49\u662f\u4ee3\u8868\u51fd\u6570\u5728\u5750\u6807\u7cfb\uff08\u6216\u5750\u6807\u5e73\u9762\uff09\u5185\u7684\u76f8\u5bf9\u4f4d\u7f6e\u53d1\u751f\u53d8\u5316\uff0c\u800c\u5bf9\u51fd\u6570\u672c\u8eab\u7684\u6027\u8d28\u548c\u5176\u4ee3\u8868\u7684\u5b9e\u9645\u610f\u4e49\u6ca1\u6709\u4efb\u4f55\u5f71\u54cd\u3002\u6bd4\u5982\uff1ay=kx+b\uff0c\u4e0a\u79fb\u6216\u4e0b\u79fb\u8868\u793a\u6574\u6761\u76f4\u7ebf\u6cbf\u7740Y\u8f74\u7684\u65b9\u5411\u5411\u4e0a\u6216\u5411\u4e0b\u5e73\u79fb\u82e5\u5e72\u4e2a\u5355\u4f4d\u3002
(1-3i)*1/2*(cosPi/3+sinPi/3i)*(cos(-Pi/6)+sin(-Pi/6)i)
=(1-3i)/2*(cosPi/6+sinPi/6i)
=1/4*3^(1/2)+3/4+(1/4*-3/4*3^(1/2))i
逆时针 (3-V3i)(Cos pi/3+ i Sin pi/3) = 3+V3i
顺时针 (3-V3i)(Cos -pi/3+i Sin -pi/3) = -2V3i
绛旓細鍒╃敤澶嶆暟涓夎褰紙鍦ㄧ櫨搴︾櫨绉戯級,鍚戦噺涓猴紙3,-鈭3锛,妯′负2鈭3,Z=r ( cos-30 + i sin-30 )=2鈭3(鈭3/2 - i/2 ) 鏃嬭浆鍚庝负Z=r(cos(-30卤60锛+ i sin(-30卤60) ),绛旀涓篫=3+鈭3 i 鎴朲=-2鈭3 i.
绛旓細绛旀閫塀锛岃窡y璐熷崐杞撮噸鍚堬紝棰樼洰鐨勬剰鎬濆氨鏄悜閲忕粫鍘熺偣鏃嬭浆锛3-鏍瑰彿3 i瀵瑰簲鍚戦噺OA=锛3锛-鏍瑰彿3锛夛紝涓巟杞寸殑澶硅涓30掳锛屾墍浠ラ『鏃堕拡鏃嬭浆60掳鍚庯紝鎭颁笌y杞寸殑璐熷崐杞撮噸鍚堬紝鏄剧劧瀹為儴涓0锛岃櫄閮ㄤ负璐燂紝鏍规嵁鎺掗櫎娉曞強鍙塀
绛旓細瀵瑰簲鐨勫鏁鏄 z=(3-i鈭3)exp(-i蟺/3)=(3-i鈭3)*(1-i鈭3)/2=-2i鈭3 閫塀 娉細澶嶆暟w閫嗘椂閽堣浆瑙抋鍚庝负w*exp(ia)
绛旓細鎵浠 z3-z1=-2鈭3-3+(2-3鈭3)i,z3=-2鈭3-3+(2-3鈭3)i+z1 =-2鈭3-3+(2-3鈭3)i+(3-2i)=-2鈭3-3鈭3i
绛旓細瑙ｏ細璁緕=a+bi 鈭碼+bi+|z|=3-鈭3i 鍗砤+|z|=3 b=-鈭3 鈭磡z|^2=a^2+b^2=(3-a)^2 鍗砨^2=9-2a 瑙ｅ緱a=-3 鈭磟=-3-鈭3i 濡傛湁鐤戦棶锛屽彲杩介棶锛
绛旓細B 鈭澶嶆暟3锛 i鐨勪竴涓緪瑙掍负锛嵪/6锛瀵瑰簲鐨勫悜閲鎸夐『鏃堕拡鏂瑰悜鏃嬭浆蟺/3锛屾墍寰楀悜閲忓搴旂殑杈愯涓猴紞蟺/2锛屾鏃跺鏁板簲涓虹函铏氭暟锛屽鐓у悇閫夋嫨椤癸紝閫夛紙B锛夈
绛旓細|z-(-3+4i)|=2 鎵浠鍒(-3,4)璺濈鏄2 鍗硓鍦ㄤ竴涓渾涓 (x+3)^2+(y-4)^2=4 |z|灏辨槸z鍒(0,0)鐨勮窛绂 鍒欒繃(-3,4),(0,0)鐨勭洿绾垮拰鍦嗙殑涓や釜浜ょ偣灏辨槸鏈杩戝拰鏈杩滆窛绂 (-3,4),(0,0)璺濈鏄5 鍦嗙殑鍗婂緞鏄2 鎵浠ユ渶杩戣窛绂绘槸5-2,鏈杩滄槸5+2 鎵浠3<=|z|<=7 ...
绛旓細鍚戦噺鍦ㄥ钩绉荤殑杩囩▼涓墍浠ｈ〃鐨澶嶆暟鏄笉鍙樼殑锛屽彧鏈夊湪鏃嬭浆鏃舵墠鏈夋墍鍙樺寲銆傚師鍚戦噺=(1-鈭3*i)*[cos(蟺/3)+i*sin(蟺/3)]=(1-鈭3*i)(1/2+鈭3/2*i)=2 銆傚疄闄呮剰涔 鍑芥暟骞崇Щ鐨勫疄闄呮剰涔夋槸浠ｈ〃鍑芥暟鍦ㄥ潗鏍囩郴锛堟垨鍧愭爣骞抽潰锛夊唴鐨勭浉瀵逛綅缃彂鐢熷彉鍖栵紝鑰屽鍑芥暟鏈韩鐨勬ц川鍜屽叾浠ｈ〃鐨勫疄闄呮剰涔夋病鏈変换浣曞奖鍝...
绛旓細鏃嬭浆鍚庣殑澶嶆暟涓簔*(cos(蟺/3)+isin(蟺/3))=(鈭3+i)(1+鈭3i)/2=2i
绛旓細(-2鈭3i) Z=(3-鈭3i)/(-2鈭3i)=[(3-鈭3i)X2鈭3i]/(2鈭3)=(6+6鈭3i)/(2鈭3)锛濃垰3+3i鍦ㄧ涓璞￠檺锛堢郴鏁伴兘涓烘鏁帮級濡傛灉婊℃剰璁板緱閲囩撼鍝︼紒浣犵殑濂借瘎鏄垜鍓嶈繘鐨勫姩鍔涖(*^__^*) 鍢诲樆鈥︹︽垜鍦ㄦ矙婕犱腑鍠濈潃鍙彛鍙箰锛屽敱鐫鍗℃媺ok锛岄獞鐫鐙瓙璧剁潃铓傝殎锛屾墜涓嬁鐫閿洏涓轰綘绛旈锛侊紒锛
