- [Maximum mark: 8]
Consider the complex number z = −1 + i.
(a) Express z in the form r e^{iθ} where −π < θ ≤ π. [2]
A and B are the points on the Argand diagram that represent the complex numbers z and z², respectively.
A is mapped onto B by the composition of a rotation and an enlargement.
(b) (i) Describe fully this mapping of A onto B, stating the scale factor of the enlargement and the angle of rotation.
(ii) Find and simplify a matrix that maps A onto B. [5]
(c) Find the smallest positive integer, n, for which zⁿ is real and positive. [1]