(A Level) Complex numbers: Cartesian form and roots

Learning objectives

Use i² = −1 to add, subtract, multiply and divide complex numbers in the form x + iy, dividing by multiplying the numerator and denominator by the conjugate

State Re z, Im z and the conjugate z*, and solve equations such as z + 2iz* = 3 − 4i by equating real and imaginary parts

Work out both square roots of a complex number such as 8 − 6i by solving (x + iy)² = a + ib for real x and y

Solve quadratic equations with complex roots, and use the fact that non-real roots of a polynomial with real coefficients occur in conjugate pairs to solve cubic and quartic equations given one complex root