On a sketch of an Argand diagram shade the region whose points represent complex numbers z satisfying the inequalities |z| ≤ 3, Rez ≥ −2 and π < arg z < π.

Throughout this question the use of a calculator is not permitted. It is given that the complex number −1 + (√3)i is …

Throughout this question the use of a calculator is not permitted. The complex number u is defined by u = 4i / (1-(√3)i)

The complex number u is defined by u = 3i / (a + 2i), where a is real.

A cyclist is travelling along a straight horizontal road at a speed of 4 ms⁻¹ when she passes a point O. She accelera…

An aeroplane is flying at a constant speed.

A particle moves in a straight line. The velocity v ms⁻¹ of the particle t s after leaving a fixed point O is given b…