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1
**Trigonometric Form of Complex Numbers**

Summary of U4 L2 I1

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**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

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**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 •

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**Find That Value, Absolutely**

Try these Graph the complex number Find the absolute value

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**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?

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**Trig Form of Complex Number**

Now we use and substitute into z = a + bi Result is Abbreviation is often

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**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 = ?

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**Product of Complex Numbers in Trig Form**

Given It can be shown that the product is Multiply the absolute values Add the θ's

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**Quotient of Complex Numbers in Trig Form**

Given It can be shown that the quotient is

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**Try It Out Try the following operations using trig form**

Convert answers to standard form

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GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS A Complex Number is in the form: z = a+bi We can graph complex numbers on the axis shown below: Real axis.

GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS A Complex Number is in the form: z = a+bi We can graph complex numbers on the axis shown below: Real axis.

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