高考问答秦始皇荆轲刺秦王片段:一道高中数学题
来源：百度文库 编辑：高考问答 时间：2024/05/03 06:59:47
设复数z满足｜z｜=1且（3+4i)z是纯虚数，求z
假设 z = a + b*i
a^2 + b^2 = 1 ....................(1)
(3 + 4*i)*z
= (3 + 4*i)(a + b*i)
= (3a - 4b) + (4a + 3b)*i
3a - 4b = 0 ........................(2)
4a + 3b ≠0 .........................(3)
(1),(2)
a = ±4/5
b = ±3/5
z = ±4/5 ± 3/5*i
z=±(4+3i)/5
假设 z = a + b*i
a^2 + b^2 = 1 ....................(1)
(3 + 4*i)*z
= (3 + 4*i)(a + b*i)
= (3a - 4b) + (4a + 3b)*i
3a - 4b = 0 ........................(2)
4a + 3b ≠0 .........................(3)
三式联立计算得出
｛a=4/5,b=3/5}或{a=-4/5,b=-3/5}
所以z=±(4+3i)/5