MAT 3730 Complex Variables Section 1.3 Vectors and Polar Forms
Preview More on Vector Representation of complex numbers Triangle Inequalities Polar form of complex numbers (Need to begin 1.4,may be?)
Recall We can identify z as the position vector
Recall We can identify z as the position vector
Triangle Inequality
Geometric Proof of the 1 st Form
(Classwork) Algebraic Proof of the 1 st Form
Geometric Proof of the 2 st Form
2nd Form from the 1 st Form
Polar Form of Complex Numbers
Recall We can identify z as the ordered pair (x,y).
Polar Form of Complex Numbers We can also use the polar coordinate
Polar Form of Complex Numbers We can also use the polar coordinate Note that is undefined if z=0.
Polar Form of Complex Numbers We can also use the polar coordinate
Example 1
Problems 1. 2.
The argument of a complex number z is not unique. is called the Principal Argument if Notation: Property of Arguments
Example 1 (Remedy)
Example 1
Polar Form of Complex Numbers We can also use the polar coordinate
Product of Complex Numbers in Polar Form
Next Class Read Section 1.4 We will introduce the Complex Exponential and Euler Formula Review Maclaurin Series (Stewart section 12.10?)