The complex number z is such that Re(z) = 1. Use your answer to part (b) to give a geometrical description of the locus of 1/z.

Verify that −1 + √2i is a root of the equation z⁴ + 3z² + 2z + 12 = 0.

The complex number u is defined by u = `(√2 – a√2i) / (1 + 2i)`, where a is a positive integer.

The polynomial x³ + 5x² + 31x + 75 is denoted by p(x).

Eddie has 16 toy cars, of which 8 are white, 5 are black and 3 are silver. He places all the cars in a bag and select…

The mass of peaches sold per day in a supermarket is normally distributed with mean 65.8kg and standard deviation 9.6kg.

Alissa has 10 different books from the series Squares and Circles. The books look similar except for their colour. Th…