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chenming68:2019-2020学年高中数学 第三章 第3课 3.2复数的四则运算(2)教学案苏教版选修1-2.doc

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2019-2020 学年高中数学 第三章 第 3 课 3.2 复数的四则运算(2) 教学案苏教版选修 1-2
教学目标: 1.掌握复数的除法及乘方运算法则及意义; 2 .理解并掌握复数进行四则运算的规律. 教学重点:复数乘方运算. 教学难点:复数运算法则在计算中的熟练应用. 教学方法:类比探究法. 教学 过程: 一、复习回顾 1.复数的加法,减法和乘法. 2.共轭复数: z ? a ? bi(a, b ? R) 与 z =a-b i 互为共轭复数;
2 2 实数的共轭复数是它本身; 共轭复数 的简单性质:z+ z =2a ;z- z =2b i ;z ? z =a +b . ? ? ? ?

二、建 构数学 * 乘方运算法则:z,z1 ,z2∈C,m,n∈N .
m n m?n (1 ) z z =z ;

(2) ( z ) =z

m n

mn

n n ; (3) ( z1 z2 )n=z1 z2 .

除法运算:z2=c+di≠0,则 三、数 学应用 例 1 计算

a+b i (a+b i)(c-d i) ac+bd bc-ad = = + 2 i. c+d i (c+d i)(c-d i) c 2+d 2 c +d 2

2-i . 3-4i

例 2 计算.

(1 +i)2=_______ ; (1 -i)2=_______ ;

1+i 1-i = _______ = _______ ; 1-i 1+i

? 1-i ? ? ? ? 1+i ?

2011

=_______ .

例 3 设 ?=- +

1 2

3 3 +?+? 2=0 ; ( 1) 1 (2) ? =1 . i ,求证: 2

结论 4

1 3 i 2 2 1+?+? 2=0

?=- + ? 3=1 ? 2=?

?=- -

2

1 2

3 i 2

1+?+? =0

? =1 ? =?
2

3

1 在复数范围内的三 个根? 思考 写出 x =

3


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