1. 5.7.3 – Division of Complex Numbers

2. We now know about adding, subtracting, and multiplying complex numbers Combining like terms Reals with reals Imaginary with imaginary When we multiply, treat as two binomials FOIL Sqaure i 2 = -1

3. Division The division of two complex numbers is a little more challenging Rule: You cannot have a complex number as the denominator (bottom) of a fraction What else cant we have in the bottom of fractions? Luckily, there is an easy to get rid of these using a specific property

4. Rationalize To rationalize the division of complex numbers, we will take use of the following property; If you have the number a +bi, the complex conjugate is a – bi Example. If you have 3 + 5i, the conjugate is 3 – 5i Property: (a + bi)(a – bi) = a 2 – b 2

5. Example. Identify the complex conjugates of the following complex numbers A) 4 + 7i B) -3 – 9i C) 10i D) 4i + 3

6. Example. Simplify the following expressions. A) (1 + 2i)(1 – 2i) B) (3 – 2i)(3 + 2i) C) (6 + 2i)(6 – 2i)

7. Division of Complex Numbers Now, from this, we can now look into how we divide complex numbers If given the complex number 6/(5 + i), we must get rid of the complex number in the bottom To do this, we will multiply top and bottom by the complex conjugate

8. Example. Simplify the expression 6/(5 + i) Short cut for multiplying the complex conjugates?

9. Example. Simplify (5 – 3i)/(1 + i)

10. Example. Simplify (2 + i)/(1 – i)

11. Assignment Pg. 265 51 – 63 all