Ten-Year-Series (TYS) Solutions | Past Year Exam Questions

1993 A Level H2 Math

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Paper 1
Paper 2
1993 A Level H2 Math Paper 1 Question 10 
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1993 TYS 1993


1993 TYS 1993


1993 TYS 1993


1993 TYS 1993

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1993 A Level H2 Math Paper 1 Question 14
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1993 A Level H2 Math Paper 2 Question 7
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1993 TYS 1993

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1993 A Level H2 Math Paper 2 Question 12 (a)

Write down the modulus and argument of the complex number $w$, where $w=1+\mathbf{i}\sqrt{3}$. Hence find the set of values of the positive integer $n$ for which ${{w}^{n}}$is real, and show that, for these values of $n$, the value of ${{w}^{n}}$ is either ${{2}^{n}}$or $-{{2}^{n}}$.

Express ${{w}^{100}}-{{\left( w* \right)}^{100}}$ in the form $k\mathbf{i}$, where $k$ is real, giving the exact value of $k$ in non-trigonometrical form.

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