X^2+1=0在复数范围X等于多少?
x^2+1=0 x^2=-1 x=i绛旓細鍦ㄥ鏁拌寖鍥鍐咃紝瀛樺湪铏氭暟鍗曚綅 i锛屾弧瓒 i² = -1锛屽洜姝ゅ彲浠ュ紩鍏ヨ櫄鏁板崟浣 i锛屾妸 x² + 1 = 0 杞寲涓 x² = -1锛岀劧鍚庤В寰 x = 卤鈭(-1) = 卤i銆傚洜姝わ紝x鐨勮В涓 x = i 鎴 x = -i銆傝繖閲岀殑 i 鍜 -i 閮芥槸澶嶆暟銆
绛旓細x²+1=0 x²=-1 x1=i x2=-i
绛旓細鍦ㄥ疄鏁拌寖鍥村唴锛屽綋鐒舵槸鏃犺В鐨勩鍦ㄥ鏁拌寖鍥鍐咃紝瑙ｅ氨鏄x=i鍜寈=-i涓や釜銆
绛旓細x²+1=0鍜寈⁴+1=0,鍦ㄦ湁鐞嗘暟闆嗗拰瀹炴暟闆嗕笂閮芥病鏈夎В銆鍦ㄥ鏁闆嗕笂锛歺²+1=0 x²=-1鏈変袱涓牴涓簒=i鎴杧=-i x⁴+1=0 x⁴=-1 x⁴=cos蟺/2+isin蟺/2 瀹冩湁鍥涗釜鏍癸細cos[(2k蟺+蟺/2)/4]+isin[锛堬級2k蟺+蟺/2锛/4] 锛坘=0,1,2,...
绛旓細x鐨勫钩鏂+1=0 鍦瀹炴暟鑼冨洿鍐呮棤瑙 濡傛灉寮曞叆铏氭暟鐨勮瘽 x=卤i i涓鸿櫄鏁板崟浣 i鐨勫钩鏂绛変簬-1
绛旓細涓嶈繃锛屽湪鏁板涓紝鎴戜滑瀹氫箟浜嗕竴涓櫄鏁板崟浣峣锛屾弧瓒筹細i² = -1鍥犳锛屾垜浠彲浠ュ皢x²+1=0鐪嬩綔鏄細x² = -1 脳 1x² = -(1 脳 1)x² = -1²x = 卤i鍥犳锛岃繖涓柟绋鍦ㄥ鏁拌寖鍥鍐呮湁涓や釜瑙ｏ紝x= i鎴杧= -i銆傝繖閲岄渶瑕佹敞鎰忕殑鏄紝澶嶆暟涓嶅睘浜庡疄鏁拌寖鍥村唴锛屽畠...
绛旓細锛1=0锛屾棤瀹炴暟瑙ｏ紝鏈澶嶆暟瑙ｃx²锛1=0鍦瀹炴暟鑼冨洿鍐呭彲浠ユ槸绌洪泦銆傚疄鏁帮紝鏄湁鐞嗘暟鍜屾棤鐞嗘暟鐨勬荤О銆傛暟瀛︿笂锛屽疄鏁板畾涔変负涓庢暟杞翠笂鐨勫疄鏁帮紝鐐圭浉瀵瑰簲鐨勬暟銆傚疄鏁板彲浠ョ洿瑙傚湴鐪嬩綔鏈夐檺灏忔暟涓庢棤闄愬皬鏁帮紝瀹炴暟鍜屾暟杞翠笂鐨勭偣涓涓瀵瑰簲銆備絾浠呬粎浠ュ垪涓剧殑鏂瑰紡涓嶈兘鎻忚堪瀹炴暟鐨勬暣浣撱傚疄鏁板拰铏氭暟鍏卞悓鏋勬垚澶嶆暟銆
绛旓細i锛/2锛寈3=锛-1-鈭3 i锛/2锛岃屽湪瀹炴暟鑼冨洿鍐呭彧鏈1涓牴x=1銆傚啀濡備竴鍏冨叚娆″疄绯绘暟鏂圭▼x^6-1=0鍦ㄥ鏁拌寖鍥鍐呮湁6涓牴锛 x1=1锛 x2=-1锛寈3=锛-1+鈭3 i锛/2锛寈4=锛-1-鈭3 i锛/2锛寈5=锛1+鈭3 i锛/2锛寈6=锛1-鈭3 i锛/2锛岃屽湪瀹炴暟鑼冨洿鍐呭彧鏈2涓牴x1=1锛寈2=-1銆
绛旓細姝ら娑夊強铏氭暟鐨勬蹇碉細铏氭暟鐨勫畾涔夛細i^2=鈥1銆備緷姝ゅ畾涔夛紝x^2=鈥1 x=鈭氣1 x=i
绛旓細鏃犺В锛孹鐨勫钩鏂逛竴瀹氭槸姝ｆ暟锛岃屾柟绋嬪寲绠涓簒鐨勫钩鏂癸紳-1,鎵浠ユ棤瑙ｏ紝缁忔楠屼负澧炴牴銆涓鍏冧簩娆℃柟绋嬬殑姹傝В鏂规硶 锛1锛夋眰鏍瑰叕寮忔硶 瀵逛簬涓鍏冧簩娆℃柟绋媋x^2+bx+c=0(a鈮0)锛屽彲鏍规嵁姹傛牴鍏紡x=(-b卤鈭氾紙b^2-4ac))/(2a)杩涜姹傝В銆傦紙2锛夊洜寮忓垎瑙ｆ硶 棣栧厛瀵规柟绋嬭繘琛岀Щ椤癸紝浣挎柟绋嬬殑鍙宠竟鍖栦负闆讹紝鐒跺悗灏嗘柟绋...
