MAT%203730%20Complex%20Variables

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MAT 3730Complex Variables

• Section 1.3
• Vectors and Polar Forms

http//myhome.spu.edu/lauw
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Preview

• More on Vector Representation of complex numbers
• Triangle Inequalities
• Polar form of complex numbers
• (Need to begin 1.4,may be?)

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Recall

• We can identify z as the position vector

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Recall

• We can identify z as the position vector

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Triangle Inequality
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Geometric Proof of the 1st Form
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Geometric Proof of the 1st Form
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(Classwork)Algebraic Proof of the 1st Form
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Geometric Proof of the 2st Form
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2nd Form from the 1st Form
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Polar Form of Complex Numbers
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Recall

• We can identify z as the ordered pair (x,y).

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Polar Form of Complex Numbers

• We can also use the polar coordinate

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Polar Form of Complex Numbers

• We can also use the polar coordinate
• Note that is undefined if z0.

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Polar Form of Complex Numbers

• We can also use the polar coordinate

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Example 1
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Problems
1. 2.
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Property of Arguments

• The argument of a complex number z is not unique.
• ? is called the Principal Argument if
• Notation

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Example 1 (Remedy)
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Example 1
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Polar Form of Complex Numbers

• We can also use the polar coordinate

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Product of Complex Numbers in Polar Form
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Next Class

• Read Section 1.4
• We will introduce the Complex Exponential and
  Euler Formula
• Review Maclaurin Series
• (Stewart section 12.10?)