A-LevelMathematicsComplex numbers9709/32 · Oct/Nov 2021 · Q36 Marks
Given the complex numbers u = a + ib and w = c + id, where a, b, c and d are real, prove that (u + w)* = u* + w*.
- (a)Given the complex numbers u = a + ib and w = c + id, where a, b, c and d are real, prove that (u + w)* = u* + w*.[2]
- (b)Solve the equation (z + 2 + i)* + (2 + i)z = 0, giving your answer in the form x + iy where x and y are real.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [B1] Substitute for u and w and state correct conjugate of one side
- [B1] Express the other side without conjugates and confirm (u+w)* = u* + w*
- [B1] Substitute and remove conjugates to obtain a correct equation in x and y
- [M1] Use i² = −1 and equate real and imaginary parts to zero
- [A1] Obtain two correct equations in x and y
- [A1] Solve and obtain answer z = −1/4 - 5/4 i
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