死算不就完了,設(shè)z1=a+bi,z2=m+ni
則z1+2z2=a+2m+(b+2n)i為純虛數(shù),則a=-2m,b≠-2n
而10（a+bi）²+5（m+ni）²=2(a+bi)(m+ni)
10a²-10b²+20abi+5m²-5n²+10mni
=2am+2ani+2bmi-2bn
10a²-10b²+5m²-5n²+(20ab+10mn)i
=2am-2bn+（2an+2bm）i
49m²-10b²-5n²+2bn=(42bm-14mn)i
等式左邊為實數(shù),右邊為虛數(shù)或零,則兩邊都為零,即42bm-14mn=0,則3b=n
而3z1+z2=3a+3bi+m+ni=-5m+(3b+n)i
我想應(yīng)該是題目出錯了,應(yīng)是
3z1-z2=-7m+(3b-n)i=-7m為實數(shù)