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

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

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. Questions?