Question

find the product of the real parts of roots of equation : `Z^2-Z=5-5i`

Answer 1

`z^2-z=5-5i`
`4z^2-4z=20-20i`
`4z^2-4z+1=21-20i`
`(2z-1)^2=(5-2i)^2`
`2z-1=pm(5-2i)`
`2z=1pm(5-2i)`
`2z=1+5-2i`
`2z=6-2i`
`z=3-i`
Real part=3
`2z=1-5+2i`
`z=-2+i`
Real part=-2
Product=3*-2=-6.