complex number 1

1. 設 z = a+ b i, w= x+ y i, a, b, x, y in R
2. |z|=1 => a^2+b^2=1
3. w = 3z+ 1/z= 3(a+b i)+ (a- b i)= 4a + 2b i
=> (x, y)=(4a, 2b) =>(a, b)=(x/4, y/2)
a^2+b^2=1 => (x/4)^2+(y/2)^2=1 即 x^2 / 16 + y^2 /4 =1 (橢圓)


2009-01-30 20:32:50 補充：
1/z = 1/(a+b i) = (a- bi)/(a^2+b^2) = a- bi

2009-01-30 20:36:28 補充：
不好意思! complex題目比較少見,搶答了3題!

1/z= (a- b i)?

Then his question is wrong

2009-01-30 20:24:23 補充：
YES,YOU ARE RIGHT

2009-01-30 20:28:05 補充：
I LOSE