1. Complex numbers – Edexcel Further Pure Mathematics 1 (FP1)
What students need to learn:
Definition of complex numbers in the form \(a + ib\) and \(r \cos \theta + i r \sin \theta\) .
The meaning of conjugate, modulus, argument, real part, imaginary part and equality of complex numbers should be known.
Sum, product and quotient of complex numbers.
\(\lvert z_1 z_2 \rvert = \lvert z_1 \rvert \lvert z_2 \rvert\)
Knowlege of the result \(\arg (z_1 z_2) = \arg z_1 + \arg z_2\) is not required.
Geometrical representation of complex numbers in the Argand diagram.
Geometrical representation of sums, products and quotients of complex numbers.
Complex solutions of quadratic equations with real coefficients.
Conjugate complex roots of polynomial equations with real coefficients.
Knowledge that if \(z_1\) is a root of \(f(z) = 0\) then \(z_1^*\) is also a root.
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