Question

For a complex number z, if Re(z) and Im(z) are the roots of x^2-7x+12=0 and z+z̅ is one of the roots of x^2–10x+16=0, then, find Re(z)-Im(z).

(a) 1

(b) -1

(c) 3

(d) -3

This question was posed to me by my school principal while I was bunking the class.

This is a very interesting question from Complex Conjugates topic in division Complex Numbers of Engineering Mathematics

Answer 1

Right option is (a) 1

Best explanation: Re(z) and Im(z) have values 3 and 4. Also 2Re(z) is either 2 or 8.

Merging, the two conditions, we get, Re(z)=4 and Im(z)=3.

∴  The required value is 4-3=1.