SPS SPS FM Pure 2025 June — Question 1 5 marks

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2025
SessionJune
Marks5
TopicComplex Numbers Arithmetic
TypeLinear equations in z and z*
DifficultyModerate -0.3 This is a straightforward complex number equation requiring substitution of z = x + iy and its conjugate, then solving simultaneous linear equations for x and y. While it involves multiple steps (substitution, equating real and imaginary parts, solving 2×2 system), the techniques are standard and mechanical with no conceptual difficulty or novel insight required, making it slightly easier than average.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide

The complex number \(z\) satisfies the equation \(z + 2iz^* = 12 + 9i\). Find \(z\), giving your answer in the form \(x + iy\). [5]

The complex number $z$ satisfies the equation $z + 2iz^* = 12 + 9i$. Find $z$, giving your answer in the form $x + iy$.
[5]

\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q1 [5]}}