1. Solve . Give your answer in form a+bi

a. Show z on an Argand diagram, find the modulus and argument of z

2. Find the set of values of x such that

3. Given . Deduce that the equation has two real roots if and it has two complex roots if

a. Determine all values of k so that has real roots

b. If and are two real roots of this equation, show that . Hence find the maximum value of

4. What is the difference between and ?