Question

If 1 – i, is a root of the equation x² + ax + b = 0, where a, b ∈ R, then find the values of a and b.

Answer 1

Sum of roots `(-a)/1` = (1 – i) + (1 + i) ⇒ a = –2  ......(Since non real complex roots occur in conjugate pairs)

Product of roots, `b/1` = (1 – i) (1 + i) ⇒ b = 2