1. Fundamentals of Engineering Analysis
EGR 1302 Unit 2, Lecture B
Approximate Running Time - 18 minutes
Distance Learning / Online Instructional Presentation
Presented by
Department of Mechanical Engineering
Baylor University
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2. The Argand Diagram Given x+yi, then (x,y) is an ordered pair. imag
real
z=x+iy x y
P(x,y)
length is the “modulus” = magnitude = absolute value
mod z = abs(z) =
real 2 3
For z=2+3i -3

3. Properties of the Magnitude of Complex Numbers
Given and find the magnitudes
Similarly

4. Adding Complex Numbers on the Argand Diagram
real 6 5 z2
Triangular Method of Addition
z3=z1+z2 2 3 z1
real
z3=z1+z2
Subtraction
real z1
-z2 z2
z3=-4-2i
Parallelogram Method of Addition z1
z2 is backwards because
of the negation

5. Polar Coordinates of Complex Numbers
on the Argand Diagram
real
“Polar Coordinates” y
(zero angle line) x
is called the “argument” or “angle”
The smallest angle is called the “principal argument”
real +
(-)
Polar Coordinates

6. Converting Between Standard Form and Polar Form of a Complex Number
real
On the Argand diagram: x y
and it is also
real
real 2

7. Complex Number Functions in the TI-89
real

8. Polar Form of the Complex Number
The Polar Form - by substituting is:
If then
recall

9. This concludes Unit 2, Lecture B