included. No particular shading convention is expected. CORE PURE: COMPLEX NUMBERS (b) Understand and use de Moivre's theorem. De Moivre's Pj12 theorem and Be able to apply de Moivre's theorem to finding multiple e.g. the expression of as a rational j13 applications angle formulae and to summing suitable series. function of . e.g. finding . The form Understand the definition and hence the form . j14 Ref. Learning outcomes Notes Notation Exclusions Specification CORE PURE: COMPLEX NUMBERS (b) Know that every non-zero complex number has n The nth j15 distinct nth roots, and that on an Argand diagram these roots of a are the vertices of a regular n-gon. complex number Know that the distinct nth roots of are: j16 for . Be able to explain why the sum of all the nth roots is j17 zero. Understand the effect of multiplication by a complex Multiplication by corresponds to Applications j18 number on an Argand diagram. enlargement with scale factor r with of complex rotation through about the origin. numbers in geometry e.g. multiplication by i corresponds to a rotation of about the origin. Be able to represent complex roots of unity on an j19 ‘Unity’ means 1.
included. No particular shading convention is expected. CORE PURE: COMPLEX NUMBERS (b) De Moivre's theorem and applications Pj12 Understand and use de Moivre's theorem. j13 Be able to apply de Moivre's theorem to finding multiple angle formulae and to summing suitable series. e.g. the expression of as a rational function of . e.g. finding . The form j14 Understand the definition and hence the form . Specification Ref. Learning outcomes Notes Notation Exclusions CORE PURE: COMPLEX NUMBERS (b) The nth roots of a complex number j15 Know that every non-zero complex number has n distinct nth roots, and that on an Argand diagram these are the vertices of a regular n-gon. j16 Know that the distinct nth roots of are: for . j17 Be able to explain why the sum of all the nth roots is zero. Applications of complex numbers in geometry j18 Understand the effect of multiplication by a complex number on an Argand diagram. Multiplication by corresponds to enlargement with scale factor r with rotation through about the origin. e.g. multiplication by i corresponds to a rotation of about the origin. j19 Be able to represent complex roots of unity on an ‘Unity’ means 1.
466635-core-pure-complex-numbers-delivery-guide-version-1-.docx