1. PART A3A - ADDITION Give the general formula for adding 2 complex numbers z1 = a + bi and z2 = c + di Give a simple example demonstrating the addition Show how to add 2 complex numbers graphically. It is not necessary to provide any numbers. This is easily done when you use the complex plane and draw the complex numbers as vectors. Resources: Dave’s Short Course, Wikipedia (look up Complex numbers), Parallelogram method, Head to Tail method. Your method should allow someone who is given z1 and z2 to “eye-ball”/sketch where z1 + z2 will be. z1 z2

2. A3B – DIVISION ALGEBRAICALLY Give the general formula/explanation for dividing 2 complex numbers z1 = a + bi and z2 = c + di Give an appropriately worked out example of division.

3. A3B GRAPHICAL DIVISION: POLAR FORM

4. REPRESENTING DIVISION GRAPHICALLY Division is a very similar operation to multiplication (meaning it involves a rotation and scaling). Search online for a definition of division in polar form. Take 2 simple complex vectors in the first quadrant (radii = 1, 2, 3, … and angles such as 90, 60, 45, 30, etc) Divide them algebraically: z1/z2 (you can use the same example you have for the first part of the problem) Convert that answer to polar form to understand what dividing by Z2 does to Z1 Draw an appropriate picture demonstrating your understanding of division in polar coordinates.

5. www.desmos.com/calculatorwww.desmos.com/calculator change window setttings to Polar and plot points by typing (1,1) or (-2,3). Use Word to draw the lines with arrows (2,0) or (2, 0 ⁰) (-2,3) or (√13, 124 ⁰) (0,3) or (3, 90 ⁰) (1,1) or (√2, 45 ⁰)

6. CONVERTING TO POLAR COORDINATES