Forum login

Not registered? Sign-up here it's free.

External links

• NCEA on TKI
• NZQA website

Calculus 3.4 Manipulate real and complex numbers, and solve equations

Achievement criteria

The level of achievement that you reach is decided by the questions that you answer correctly.

Achievement

• You manipulate real and complex numbers, and solve equations.
• Manipulation will be based on a selection from:
  • conversion between polar and rectangular forms of real and complex numbers
  • simplification of sums, differences, products, and quotients of surds or complex numbers expressed in rectangular form
  • simplification of products or quotients of complex numbers expressed in polar form
  • use of de Moivre’s theorem in the simplification of expressions such as .
• Equations will be based on a selection from:
  • quadratic
  • cubic (limited to rational roots only)
  • exponential, such as 2^3x+1=5
  • logarithmic, such as ln(x + 5) = 1.34 (any base).
• You are expected to have a knowledge of:
  • the remainder and factor theorem
  • the process of completing the square.

Achievement with Merit

• You need to reach Achievement.
• You solve more complicated equations which are based on a selection of those equations identified for achievement, plus:
  • irrational equations, such as
  • cubic equations with one integer root and two complex roots
  • equations of the form , zⁿ = a + bi where a, b are real and n is a positive integer.

Achievement with Excellence

• You need to reach Achievement with Merit.
• You solve problem(s) involving real or complex numbers that may require a chain of reasoning.
• Problems may include:
  • algebraic proofs
  • loci – geometric representation of complex numbers
  • multi-step equations
  • binomial expansions for small positive integer exponents.

Back to top