1. Aims: To know what the complex number i is. To be able to simplify complex numbers. To be able to add, subtract and multiply complex numbers. To know what a conjugate complex number is. Complex Numbers Lesson 1

2. Complex Numbers - Introduction Imaginary Numbers

3. Complex Numbers - Introduction Express in terms of i: 1.√(-64)2. √(-7) 3.√16 - √(-81)4. 3 - √(-25) 5.√(-100) - √(-49) Simplify 1.i 3 2. i 7 3.i -9 4. i(2i – 3i 3 ) 5. (i + 2i 2 )(3 – i) 10 minutes – have a go!

4. Manipulation of Complex Numbers A complex number is Real partImaginary part Notes : 1.The complex conjugate of a complex number a + ib is a – ib 2.When a complex number is multiplied by its conjugate the answer is just REAL (a + ib)(a – ib) = 3.When adding complex numbers just add/subtract the real and imaginary parts separately. Eg. (2 + 3i) + (7 – 6i) =

5. Manipulation of Complex Numbers 4.Multiplying complex numbers just uses basic rules of algebra e.g. (4 – 3i)( -7 + 5i) =

6. Manipulation of Complex Numbers Mixed Example A complex number is z = 3 – 2i a)What is it’s conjugate, z*? b)What is the sum of z and z* ? c)What is z – z* d)What is the product of z and z* e)Can you make any general statements about parts b) to d) Do exercise 7A page 100 5 mins have a go!

7. Finally!