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Trigonometric Form of Complex Numbers Summary of U4 L2 I1.

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Presentation on theme: "Trigonometric Form of Complex Numbers Summary of U4 L2 I1."— Presentation transcript:

1 Trigonometric Form of Complex Numbers Summary of U4 L2 I1

2 2 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

3 3 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

4 4 Find That Value, Absolutely Try these Graph the complex number Find the absolute value

5 5 Trig Form of Complex Number Consider the graphical representation We note that a right triangle is formed a + bi θ b a r How do we determine θ?

6 6 Trig Form of Complex Number Now we use and substitute into z = a + bi Result is Abbreviation is often

7 7 Try It Out Given the complex number -5 + 6i Write in trigonometric form r = ? θ = ? Given z = 3 cis 315° Write in standanrd form r = ? a = ? b = ?

8 8 Product of Complex Numbers in Trig Form Given It can be shown that the product is Multiply the absolute values Add the θ's

9 9 Quotient of Complex Numbers in Trig Form Given It can be shown that the quotient is

10 10 Try It Out Try the following operations using trig form Convert answers to standard form


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