1. Trig 2.3 Polar Coordinates
Objective: to convert rectangular coordinates to polar and vice versa

2. Review Complex Plane
Imagine that you are walking to the point 2 + 3i. Instead of walking 2 units right, turning 90⁰, and walking 3 more units, you want to take the nearest route. You need to have a direction and a distance to walk. What is the direction you need to take? How far should you walk?

3. Polar Coordinates
Every polar coordinate has both an angle (direction) and a radius (distance). (r, θ) Partner Work – each group needs a balloon, two rubber bands, and a permanent marker. One person will be the coach, the other is the recorder.

4. Plot the Points (4, 0⁰) (2, 3π/2) (-2, 210⁰) (3, 135⁰)
Now, on paper, plot the following points:
(4, 30o)
(-4, 225o)
(2, -300o)
(-3, -270o)

5. Polar Form of Complex Numbers
The polar form or trigonometric form of the complex number a + bi is r(cos θ + i sin θ).
To express i in polar form, first find the radius and the argument.
r = √( ) θ = tan-1(4/-3) QII
-3 + 4i = 5(cos i sin 2.21)
= 5 cis 2.21
Express 2 – 2i√5 in polar form.
Express 1 + √3i in polar form.

6. From Polar Form to Rectangular
a = r cos θ and b = r sin θ
Express 5 cis π/6 in rectangular form.
x = 5 cos 30⁰ y = 5 sin 30⁰
x = 5 (√(3)/2) y = 5 (1/2)
5√3/2 + 5/2 i
Express 10 cis 300⁰ in rectangular form.
Express 4 cis 135o in rectangular form.

7. Practice Problems Assignment page 95 8, 9a, 10, 15
Find the magnitude and argument of each of the following numbers.
2√3 – 2i
4 cis 300o
If z = 5 cis 75o and w = 2 cis 100o, find |zw| and arg(zw).
Assignment page 95 8, 9a, 10, 15