Find the square roots of the following: `7-24 i` (ii) `5+12 i`

Answer

N/a

Explanation

Let `sqrt(5+12i)=x+iy`
`rArr" "5+12i=(x+iy)^(2)`
` " "=x^(2) +i^(2)y^(2)+2ixy`
`" "=x^(2)-y^(2)+2ixy`
`rArr" "x^(2)-y^(2)=5" "`...(1)
and `" "2xy=12" "`...(2)
Now, `" "(x^(2)+y^(2))^(2)=(x^(2)-y^(2))^(2)+(2xy)^(2)`
`" "=5^(2)+12^(2)`
`" "=169`
`rArr" "x^(2)+y^(2)=13" " `...(3)
Adding eqs. (1) and (3)
`" "2x^(2)=18`
`rArr" "x^(2)=9`
`rArr" "x=pm3`
In eq. (2), putting `x=pm3`
`" "2(pm3)y=12`
`rArr" "y=pm2`
`therefore" "` The square roots of `(5+12i)=pm(3+2i)`.