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Expressing Various Complex Numbers in Exponential Form Express the following complex numbers in the form $z=r{{e}^{text{i}theta }}$, where $rge 0$ and $-pi <theta le pi $, (i) $frac{cos theta +text{i}sin
Expressing sin θ + i cos θ as r e^(iθ) and other variations Express the following complex numbers in the form $z=r{{e}^{text{i}theta }}$, where $rge 0$ and $-pi <theta le
2022 RI P2 Q2 Do not use a calculator in answering this question. (a) Let $text{f}left( z right)$ be a polynomial in $z$ of degree $4$ with real coefficients. The
2022 RI P1 Q5 Do not use a calculator in answering this question. The complex numbers $z$ and $w$ are given by $z=sin left( frac{pi }{6} right)+text{i}cos left( frac{pi }{6}
2022 NJC P1 Q8 Two complex numbers are $z=2left( cos frac{pi }{4}-text{i}sin frac{pi }{4} right)$ and $w=left( -text{i}sqrt{3} right)z$. (i) Show that $z+{{w}^{*}}=r{{text{e}}^{text{i}left( frac{3pi }{4} right)}}$ for some positive constant
These Ten-Year-Series (TYS) worked solutions with video explanations for 2004 A Level H2 Mathematics Paper 1 Question 12 are suggested by Mr Gan. For any comments or suggestions please contact
These Ten-Year-Series (TYS) worked solutions with video explanations for 2005 A Level H2 Mathematics Paper 2 Question 1 are suggested by Mr Gan. For any comments or suggestions please contact
These Ten-Year-Series (TYS) worked solutions with video explanations for 2006 A Level H2 Mathematics Paper 1 Question 6 are suggested by Mr Gan. For any comments or suggestions please contact
2018 CJC P1 Q11 It is given that $z=-frac{1}{2}$ is a root of the equation $8{{z}^{3}}+left( 4-4sqrt{2} right){{z}^{2}}+left( 2-2sqrt{2} right)z+1=0$ The roots of the equation are denoted by ${{z}_{1}}$, ${{z}_{2}}$,
2021 TMJC P1 Q4 A quartic (degree four) polynomial $text{P}left( z right)={{z}^{4}}+a{{z}^{3}}+b{{z}^{2}}+cz+d$ has real coefficients. The equation $text{P}left( z right)=0$ has root $r{{text{e}}^{mathbf{i}theta }}$, where $r>0$ and $0<theta <pi $.