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 Procedures: Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” You will hear “CHIMES” at the completion of the audio portion of each slide; hit the “Enter” key, or the “Page Down” key, or “Left Click” You may exit the slide show at any time with the “Esc” key; and you may select and replay any slide, by navigating with the “Page Up/Down” keys, and then hitting “Shift+F5”.

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

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

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

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

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

Complex Number Functions in the TI-89 real

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

This concludes Unit 2, Lecture B