8.2 Trigonometric (Polar) Form of Complex Numbers

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

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.

You try! (4 + i) + (1 + 3i)

II. Trigonometric (Polar) Form

θ

r

x

y

θ = direction angle

r = magnitude

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

Example 2 Express 2(cos 300° + i sin 300°) in

rectangular form. (standard form)

Refer to the unit circle Use your calculator to confirm

You try… Express 6 cis 135° in rectangular form.

(standard form)

Homework Pages 345 – 346 #3 - 35 odd

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