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For a complex number z, if Re(z) and Im(z) are the roots of x2-7x+12=0 and z+z̅ is one of the roots of x2–10x+16=0, then, find Re(z)-Im(z).

For a complex number z, if Re(z) and Im(z) are the roots of x2-7x+12=0 and z+z̅ is one of the roots of x2–10x+16=0, then, find Re(z)-Im(z). Correct Answer 1

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.

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