已知z1=1-3i,z2=6-8i,若1/z+1/z1=1/z2,求z的值

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已知z1=1-3i,z2=6-8i,若1/z+1/z1=1/z2,求z的值
已知z1=1-3i,z2=6-8i,若1/z+1/z1=1/z2,求z的值

已知z1=1-3i,z2=6-8i,若1/z+1/z1=1/z2,求z的值
1/z=1/z2-1/z1
=1/(6-8i)-1/(1-3i)
=(6+8i)/(6+8i)(6-8i)-(1+3i)/(1+3i)(1-3i)
=(6+8i)/(36+64)-(1+3i)/(1+9)
=(6+8i)/100-(1+3i)/10
=(-2-11i)/50
z=50/(-2-11i)
=50(-2+11i)/(-2+11i)(-2-11i)
=50(-2+11i)/(4+121)
=(-4+22i)/5