MathematicsCode 9709
Complex numbers
What this topic asks you to be able to do
- understand what a complex number is, recall what the terms real part, imaginary part, modulus, argument and conjugate mean, and use the fact that a pair of complex numbers is equal if and only if their real parts are equal and their imaginary parts are equal
- carry out each of the four operations, adding, subtracting, multiplying and dividing, on a pair of complex numbers written in the Cartesian form x + iy
- apply the fact that non-real roots of a polynomial equation whose coefficients are real come in conjugate pairs
- represent complex numbers in geometric form on an Argand diagram
- carry out both multiplication and division on a pair of complex numbers in polar form, written r(cosθ + i sinθ) or re^{iθ}
- work out the two square roots that a complex number has
- understand, in plain language, what happens geometrically when a complex number is conjugated, and what happens when two complex numbers are added, subtracted, multiplied or divided
- use loci on an Argand diagram to show simple equations and inequalities that involve complex numbers