设复数z满足|z|=1,且(3+4i)z是纯虚数,则杠z=_.

设复数z满足|z|=1,且(3+4i)z是纯虚数,则杠z=_.
设复数z满足|z|=1,且(3+4i)z是纯虚数,则杠z=_.

设复数z满足|z|=1,且(3+4i)z是纯虚数,则杠z=_.
设z=a+bi
(3＋4i)z=(3X-4Y)+(4X+3Y)i
Z是纯虚数,3X-4Y=0
｜z｜＝1
X=4/5
Y=3/5
或X=-4/5
Y=-3/5
Z上面一横=4/5-3/5i
或-4/5+3/5i