# Trigonometric Form of Complex Numbers

## Presentation on theme: "Trigonometric Form of Complex Numbers"— Presentation transcript:

Trigonometric Form of Complex Numbers
Summary of U4 L2 I1

Graphical Representation of a Complex Number
Graph in coordinate plane Called the complex plane Horizontal axis is the real axis Vertical axis is the imaginary axis 3 + 4i • -2 + 3i • • -5i

Absolute Value of a Complex Number
Defined as the length of the line segment From the origin To the point Calculated by using Pythagorean Theorem 3 + 4i •

Find That Value, Absolutely
Try these Graph the complex number Find the absolute value

Trig Form of Complex Number
Consider the graphical representation We note that a right triangle is formed a + bi • r b θ a How do we determine θ?

Trig Form of Complex Number
Now we use and substitute into z = a + bi Result is Abbreviation is often

Try It Out Given the complex number -5 + 6i Given z = 3 cis 315°
Write in trigonometric form r = ? θ = ? Given z = 3 cis 315° Write in standanrd form a = ? b = ?

Product of Complex Numbers in Trig Form
Given It can be shown that the product is Multiply the absolute values Add the θ's

Quotient of Complex Numbers in Trig Form
Given It can be shown that the quotient is

Try It Out Try the following operations using trig form