Moderate -0.5 This is a straightforward complex number equation requiring substitution of z = x + iy and z* = x - iy, then equating real and imaginary parts to solve a simple 2×2 system. While it's a Further Maths topic, the technique is routine and mechanical with no conceptual difficulty beyond the standard method.
Question 4:
4 | Uses correct conjugate of z
and expresses equation in
terms of and where
and are real | AO1.1a | M1 | z = x+iy
2 ( x+iy )−5i ( x−iy )=12
Re: 2x−5y =12
Im: 2y−5x=0⇒ y =2.5x
2x−12.5x=12
8 20
x=− and y =−
7 7
8 20
z =− − i
7 7
Equates 𝑥𝑥real an𝑦𝑦d imaginary
p𝑥𝑥arts of𝑦𝑦 their equation
(conjugate might be
wrong). | AO1.1a | M1
Solves their equations
correctly for and having
used the correct conjugate
of z 𝑥𝑥 𝑦𝑦 | AO1.1a | M1
States a fully correct
solution, must be z =… | AO1.1b | A1
Total | 4
Q | Marking Instructions | AO | Marks | Typical solution