已知复数Z的模=2, 求复数1+根号3 i+Z的模的最大值和最小值

问题描述:

已知复数Z的模=2, 求复数1+根号3 i+Z的模的最大值和最小值

|1+√3i|-|z|≤|1+√3i+z|≤|1+√3i|+|z|
即0≤|1+√3i+z|≤4
当z=-(1+√3i)时,|1+√3i+z|取最小值
当z=1+√3i 时,|1+√3i+z|取最大值