Question

यदि `z_(1)=2-i,z_(2)=1+i`, तब `|{:(z_(1)+z_(2)+1)/(z_(1)-z_(2)+i):}|` का मान ज्ञात कीजिए ।

Answer 1

`|(z_(1)+z_(2)+1)/(z_(1)-z_(2)+i)|=|(2-i+1+i+1)/(2-i-1-i+i)|`
`=|(4)/(1-i)|=|(4(1-i))/((1-i)(1+i))|`
`=|(4+4i)/(1-i^(2))|=|(4+4i)/(2)|`
`=|2+2i|=sqrt(2^(2)+2^(2))=2sqrt(2)`