1. 8.2 Trigonometric (Polar) Form of Complex Numbers

2. I.The Complex Plane & Vector Representation  Unlike real numbers, complex numbers cannot be ordered.  One way to organize or illustrate them is by using a graph.  Initial point (0,0)  Terminal point (a,b) Imaginary axis Real axis

3. Example 1  Find the sum of 6 – 2i and -4 – 3i. Graph both complex numbers and their resultant.  Note: This geometric representation is why a + bi is called rectangular form.

4. You try!  (4 + i) + (1 + 3i)

5. II. Trigonometric (Polar) Form θ r x y θ = direction angle r = magnitude

6. Trigonometric (Polar) Form of a Complex Number x + yi = r cos θ + r sin θ ∙ i = r(cos θ + i sin θ) abbreviated…r cis θ

7. Example 2  Express 2(cos 300° + i sin 300°) in rectangular form. (standard form)  Refer to the unit circle  Use your calculator to confirm

8. You try…  Express 6 cis 135° in rectangular form. (standard form)

9. Homework  Pages 345 – 346 #3 - 35 odd  GET IT DONE