2-3 /
Ch2
88
i 88 (1)(2) (1)(2)(3)
89()a, b , a b
89()a, b , a b 4,0,1+ 2i, 3i
89()a, b , a b 40, 1 + 2i 3i
89()a, b , a b 3i
89()a, b, c, d a, b
189a, b a, b
190a, b a, b
90()a, b, c, d
290
290
91
391
i k0.91
392
92
(c,d0) 92
4a+bi a, b92
4a+bi a, b92
4a+bi a, b92
93()
93
593
593
594
594
94()
695
695
95
95
796 ,
796 ,
796 ,
796 ,
796 ,
796 ,
97()f(x)n f(x) = 0 nf() =0f(x) = 0n f(x)=3x5=0 f(x)=0 ()
97()f(x)n f(x) = 0 nf() =0f(x) = 0n g(x)=x2+1=0 g(i)=g(i)=0
iig(x)=0 ()
897a. x=2ix3+x2+4x+a=0 f(x)=x3+x2+4x+a f(2i)=0 8i4+8i+a=0
898 x32x2+x2=0(2)2.(3) i.(4) i.(5) 1+i. (1) (2)(3)(4)
98()n .(kk)nn. (1)
99()f(x) f(x)=0 f(x)=0. :f(x)
99()f(x)=0
9100 x43x3+6x2+ax+b=013i(1)ab (2) (1) f(x) = x43x3+6x2+ax+b
=(x(13i))(x(1+3i))
9100(1) f(x) = x43x3+6x2+ax+b q(x)
9100(1) f(x) = x43x3+6x2+ax+b (2) f(x)=0
999 . f(x) = x45x3+8x2x5 =(x(2+i))(x(2i)) 2+ix45x3+8x2x5=0
999f(x) = x45x3+8x2x5 q(x)
999f(x) = x45x3+8x2x5
101(2) n(n 1)(1)
101()()
10102f(x)=2x33x28x3=0. 012 3 8 3 5 225 3 3f(x)=013
11 2102 f(x) = 2x4+x37x29x+6=0. 0 6 3 0 32 1 7 9 6 102 4 5 3 62
5 3 3 3216 6 1 3 3
11 2101 f(x) = 2x4+x37x29x+6=0. 0 6 3 0 32 1 7 9 6 102 4 5 3 62
5 3 3 3216 6 1 3 3f(x)=(x2)(2x1)(x2+3x+3) = 0
11101 f(x) = 2x4+x37x29x+6=0. f(x)=(x2)(2x1)(x2+3x+3) = 0
11103f(x)=2x3+7x27x5=0 2 5 02 7 7 5 32 1610 1 3 5
103() f(x)=0 a b . f(x) = 0 a b f(a)f(b) 0f(a)f(b)
12105 x38x+1 = 0 f(x) = x38x+1 3201 23
12105 x3 + x2 2x 1 = 0 f(x) = x3 + x2 2x 1 2 1 1012
13105 x3 8x + 1 = 0 f(x) = x3 8x + 1
13105 x3 + x2 2x 1 = 0 f(x) = x3 + x2 2x 1
14106 f(x) 1 1, 2, 3
14106 f(x)
15106a>0n xn = a (1) f(x)=xn a xn = a 0 a + 1f (x) = 0
15107a>0n xn = a (2) xn = a ()()(1) (2)xn = a
n 107an a>0nn a n x3 = 5 3 353 53
15107(1) x4=16 (2)
