Question

Find the modulus of each of the following :
`{:((i),(3+sqrt(-5)),(ii),(-3-4i),(iii),(7+24i),(iv),3i),((v),((3+2i)^(2))/((4-3i)),(vi),((2-i)(1+i))/((1+i)),(vii),5,(viii),(1+2i)(i-1)):}`

Answer 1

Correct Answer - `{:((i),sqrt(14),(ii),5,(iii),25,"(iv)",3),((v),(13)/(5),(vi),sqrt(5),(vii),5,"(viii)",sqrt(10)):}`
`(v)" "z =((3+2i)^(2))/((4-3i))=((9+4i^(2)+12i))/((4-3i))=((5+12i))/((4-3i))xx((4+3i))/((4+3i))=(-16+63i)/(25)`
`rArr" "|z|^(2)={((-16)/(25))^(2)+((63)/(25))^(2)}=((256)/(625)+(3969)/(625))=(4225)/(625)`
`rArr" "|z| = sqrt((4225)/(625))=(65)/(25)=(13)/(5)`.
`(vi)" "z =((2-i)(1+i))/((1-i))=((3+i))/((1-i))xx((1+i))/((1+i))=((2+4i))/(2)=(1+2i)`.