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LearnEdexcelYFM012018 specificationWFM01 · Further Pure Mathematics 1Complex numbers
WFM01 · Module

Complex numbers

3 subtopics≈ 110 min in total
Start the module: Arithmetic and conjugatesOpen graphing calculator

  1. Arithmetic and conjugates

    Meet ii, where i2=−1i^2=-1. Add, subtract and multiply complex numbers like brackets, divide using the conjugate, and solve equations by equating real and imaginary parts.

    ≈ 35 min

  2. The Argand diagram, modulus and argument

    Plot z=x+iyz=x+iy as the point (x,y)(x,y). Its distance from the origin is the modulus ∣z∣|z|, and its angle from the positive real axis is the argument arg⁡z\arg z, with −π<arg⁡z≤π-\pi<\arg z\le\pi.

    ≈ 35 min

  3. Polynomial equations and square roots

    Every quadratic now has two roots. For polynomials with real coefficients, complex roots come in conjugate pairs, which lets you find all the roots from one. Square roots of a+bia+bi come from equating real and imaginary parts.

    ≈ 40 min