Solve the quadratic equation (3 + i)w² – 2w + 3 − i = 0, giving your answers in the form x + iy, where x and y are real.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] Use quadratic formula to solve for w.
2. [M1] Use i² = -1 in (3 + i)(3 - i).
3. [A1] Obtain one of the answers w = (2+6i)/(6+2i) or w = (2-6i)/(6+2i). Must be simplified to this form.
4. [M1] Show intention to multiply numerator and denominator by conjugate of their denominator. Independent of previous M marks but must be of the same form, e.g. a/(b+ci).
5. [A1] Obtain final answers 3/5 + 4/5 i and -i. Accept 0.6 + 0.8i and 0 – i. SC Both correct final answers from w = (2+6i)/(6+2i) and w = (2-6i)/(6+2i) seen, no evidence of conjugate, then SC B1 for both. Allow x = 3/5, y = 4/5 or x = 0, y = -1. A0 for (3+4i)/5.