复数z满足2z+丨z丨=3+6i 求复数z
问题描述:
复数z满足2z+丨z丨=3+6i 求复数z
答
2z+|z|=3+6i
则复数z的虚部是3i,设:z=a+3i,则:
2(a+3i)+|z|=3+6i
2a+|z|=3
3-2a=|z|
(3-2a)²=|z|²=a²+9
3a²-12a=0
a=0或a=4【舍去】
得:z=3i