高中数学第五章数系的扩充与复数的引入5.2复数的四则运算5.2.2复数的乘法与除法省公开课一等奖新名.pptx

-,*,-,1,Z,HISHISHULI,知识梳理,S,UITANGYANLIAN,随堂演练,D,IANLITOUXI,典例透析,目标导航,Z,HISHISHULI,知识梳理,S,UITANGYANLIAN,随堂演练,D,IANLITOUXI,典例透析,目标导航,Z,HISHISHULI,知识梳理,S,UITANGYANLIAN,随堂演练,D,IANLITOUXI,典例透析,目标导航,Z,HISHISHULI,知识梳理,S,UITANGYANLIAN,随堂演练,D,IANLITOUXI,典例透析,目标导航,Z,HISHI SHULI,知识梳理,S,UITANGYANLIAN,随堂演练,D,IANLI TOUXI,典例透析,M,UBIAODAOHANG,目标导航,2,.,2,复数乘法与除法,1/26,1,.,掌握复数乘法法则,能熟练地进行复数乘法运算,.,2,.,了解共轭复数概念,会解答相关共轭复数简单问题,.,3,.,掌握复数除法法则,能熟练地进行复数除法运算,.,2/26,1,.,复数乘法,(1),复数乘法定义,设,a+b,i(,a,b,R,),与,c+d,i(,c,d,R,),分别是任意两个复数,我们定义复数乘法以下,:(,a+b,i)(,c+d,i),=,(,ac-bd,),+,(,ad+bc,)i,.,也就是说,两个复数积依然是一个复数,.,复数乘法与,多项式,乘法是类似,但在运算过程中,需要用,i,2,=-,1,进行化简,然后把实部与虚部分别合并,.,3/26,(2),复数乘法运算律,复数乘法满足交换律、结合律以及乘法对加法分配律,.,对任何,z,1,z,2,z,3,C,有,z,1,z,2,=z,2,z,1,(,交换律,);,(,z,1,z,2,),z,3,=z,1,(,z,2,z,3,)(,结合律,);,z,1,(,z,2,+z,3,),=z,1,z,2,+z,1,z,3,(,分配律,),.,(3),复数乘方,对于任意,z,z,1,z,2,C,m,n,N,+,有,z,m,z,n,=z,m+n,;,(,z,m,),n,=z,mn,;,4/26,5/26,6/26,7/26,8/26,9/26,题型一,题型二,题型三,题型四,【例,1,】,计算,:,(1)(2,+,i)(2,-,i);,(2)(1,+,2i),2,;,(3)(3,+,2i)(1,-,3i),.,分析,:,按照多项式乘法进行,计算,并把,i,2,化为,-,1,.,解,:,(1)(2,+,i)(2,-,i),=,2,2,-,i,2,=,4,+,1,=,5,.,(2)(1,+,2i),2,=,1,+,4i,+,4i,2,=-,3,+,4i,.,(3)(3,+,2i)(1,-,3i),=,3,+,(2,-,9)i,-,6i,2,=,9,-,7i,.,10/26,题型一,题型二,题型三,题型四,方法总结,1,.,复数乘法能够按照多项式乘法法则进行,注意选取恰当乘法公式进行简便运算,比如平方差公式、完全平方公式等,.,2,.,像,3,+,4i,和,3,-,4i,这么两个复数叫作互为共轭复数,其形态特征为,a+b,i,和,a-b,i,其数值特征为,(,a+b,i)(,a-b,i),=a,2,+b,2,.,11/26,题型一,题型二,题型三,题型四,【变式训练,1,】,计算,:(1)(1,+,i),2,;,(2)(3,+,4i)(3,-,4i);,(3)(1,-,2i)(3,+,4i)(,-,2,+,i),.,解,:,(1)(1,+,i),2,=,1,+,2i,+,i,2,=,2i,.,(2)(3,+,4i)(3,-,4i),=,9,-,(4i),2,=,25,.,(3)(1,-,2i)(3,+,4i)(,-,2,+,i),=,(3,+,4i,-,6i,-,8i,2,)(,-,2,+,i),=,(11,-,2i)(,-,2,+,i),=-,22,+,11i,+,4i,-,2i,2,=-,20,+,15i,.,12/26,题型一,题型二,题型三,题型四,13/26,题型一,题型二,题型三,题型四,14/26,题型一,题型二,题型三,题型四,15/26,题型一,题型二,题型三,题型四,16/26,题型一,题型二,题型三,题型四,反思,将复数问题转化为实数问题是解复数题惯用、主要方法,.,17/26,题型一,题型二,题型三,题型四,18/26,题型一,题型二,题型三,题型四,19/26,题型一,题型二,题型三,题型四,20/26,题型一,题型二,题型三,题型四,21/26,1 2 3 4 5,1,已知,i,是虚数单位,则,(,-,1,+,i)(2,-,i),=,(,),A.,-,3,+,iB.,-,1,+,3i,C.,-,3,+,3iD.,-,1,+,i,解析,:,(,-,1,+,i)(2,-,i),=-,2,+,i,+,2i,-,i,2,=-,1,+,3i,故选,B,.,答案,:,B,22/26,1 2 3 4 5,23/26,1 2 3 4 5,24/26,1 2 3 4 5,25/26,1 2 3 4 5,26/26,