OCR FP1 2010 January — Question 3 5 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicComplex Numbers Arithmetic
TypeLinear equations in z and z*
DifficultyModerate -0.3 This is a straightforward Further Maths FP1 question requiring students to substitute z = x + iy and z* = x - iy, then equate real and imaginary parts to solve a simple system of two linear equations. While it's a Further Maths topic, the algebraic manipulation is routine and mechanical with no conceptual challenges, making it slightly easier than average overall.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02e Arithmetic of complex numbers: add, subtract, multiply, divide

3 The complex number \(z\) satisfies the equation \(z + 2 \mathrm { i } z ^ { * } = 12 + 9 \mathrm { i }\). Find \(z\), giving your answer in the form \(x + \mathrm { i } y\).

3 The complex number $z$ satisfies the equation $z + 2 \mathrm { i } z ^ { * } = 12 + 9 \mathrm { i }$. Find $z$, giving your answer in the form $x + \mathrm { i } y$.

\hfill \mbox{\textit{OCR FP1 2010 Q3 [5]}}