Pure Mathematics Unit Two

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  Complex Numbers and Calculus II

  • express complex numbers in the form a + ib, a, b, ∊ ℝ 
  • calculate the square root of a complex number 
  • carry out the algebra of complex numbers (add, subtract, multiply, divide) 
  • calculate the complex roots of a polynomial 
  • find the modulus of a complex number 
  • find the argument of a complex number 
  • understand the properties of modulus and argument 
  • interpret the modulus and argument of complex numbers 
  • represent complex numbers on an Argand diagram (including sums, differences, products and quotients) 
  • identify and sketch loci on an Argand diagram  
  • oivre’s theorem for n ∊ ℤ+
  • establish that e^iθ = cos θ + i sin θ
    
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