OCR FP1 2015 June — Question 1 3 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
Marks3
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Mark schemeDownload PDF ↗
TopicComplex Numbers Arithmetic
TypeReal and imaginary part expressions
DifficultyModerate -0.8 This is a straightforward application of basic complex number definitions: z* = x - iy and |z|² = x² + y². The algebra is simple (3(x² + y²) - (x² + y²) = 2x² + 2y²) with no problem-solving required, just routine manipulation of standard formulas.
Spec4.02a Complex numbers: real/imaginary parts, modulus, argument4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z)
1 The complex number \(x + \mathrm { i } y\) is denoted by \(z\). Express \(3 z z ^ { * } - | z | ^ { 2 }\) in terms of \(x\) and \(y\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(z^* = x - iy\)B1 Conjugate stated or used
\(z = \sqrt{x^2 + y^2}\)
\(2(x^2 + y^2)\)B1 Obtain correct answer, a.e.f. but not involving \(i\)
[3] 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $z^* = x - iy$ | B1 | Conjugate stated or used |
| $|z| = \sqrt{x^2 + y^2}$ | B1 | Modulus or its square stated or used |
| $2(x^2 + y^2)$ | B1 | Obtain correct answer, a.e.f. but not involving $i$ |
| **[3]** | | |

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1 The complex number $x + \mathrm { i } y$ is denoted by $z$. Express $3 z z ^ { * } - | z | ^ { 2 }$ in terms of $x$ and $y$.

\hfill \mbox{\textit{OCR FP1 2015 Q1 [3]}}
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