complex number問題

2009-11-08 3:25 am

回答 (1)

2009-11-08 3:59 am
✔ 最佳答案
(a) z(1+i)^4=(a+3i)^2
|z(1+i)^4|=|(a+3i)^2|
Since |(1+i)|=√2
We have 3*4=a^2+9=>a=-√3

(b) (1+I)^4=4[cosπ+isinπ]=-4
(-√3+3i)^2=12[cos5π/3+isin5π/3]
So z=-3[cos5π/3+isin5π/3] which shows that the required smallest number is n=3


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