Complex Numbers Part 1

Given, root of z2+αz+β=0 is 1−2i.
Since, it is quadratic equation and one root is complex in nature, its another root is complex conjugate.
∴ Two roots are 1−2i and 1+2i.
Now, sum of roots =−‌

α

1

=−α
=(1−2i)+(1+2i)=2
Gives, α=−2
Product of roots =‌

β

1

=β
Gives, β=5=(1−2i)(1+2i)=1+4=5
Gives, β=5 ∴‌‌α−β=−2−5=−7