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Fundamentals of Engineering Analysis - Polar Form of a Complex Number

This online instructional presentation by Baylor University's Department of Mechanical Engineering covers the polar form of complex numbers, including properties, addition, subtraction, and conversion between standard and polar forms.

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Fundamentals of Engineering Analysis - Polar Form of a Complex Number

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  1. Fundamentals of Engineering Analysis EGR 1302 - Polar Form of a Complex Number 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”.

  2. P(x,y) y length is the “modulus” = magnitude = absolute value real x 3 real 2 -3 The Argand Diagram Given x+yi, then (x,y) is an ordered pair. imag z=x+iy mod z = abs(z) = For z=2+3i

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

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

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

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

  7. real Complex Number Functions in the TI-89

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

  9. This concludes the Lecture

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