© 2005 Baylor University Slide 1 Fundamentals of Engineering Analysis EGR 1302 - Polar Form of a Complex Number.

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© 2005 Baylor University Slide 1 Fundamentals of Engineering Analysis EGR Polar Form of a Complex Number

© 2005 Baylor University Slide 2 The Argand Diagram Given x+yi, then (x,y) is an ordered pair. real imag z=x+iy x y P(x,y) length is the “modulus” = magnitude = absolute value mod z = abs(z) = For z=2+3i real

© 2005 Baylor University Slide 3 Properties of the Magnitude of Complex Numbers Given and find the magnitudes Similarly

© 2005 Baylor University Slide 4 Adding Complex Numbers on the Argand Diagram Triangular Method of Addition real 2 3 z1z1 6 5 z2z2 z 3 =z 1 +z 2 real z1z1 z2z2 z 3 =z 1 +z 2 Parallelogram Method of Addition real z1z1 -z 2 z 3 =-4-2i Subtraction z2 is backwards because of the negation

© 2005 Baylor University Slide 5 real Polar Coordinates of Complex Numbers on the Argand Diagram x y (zero angle line) “Polar Coordinates” is called the “argument” or “angle” The smallest angle is called the “principal argument” real + (-) Polar Coordinates

© 2005 Baylor University Slide 6 real Converting Between Standard Form and Polar Form of a Complex Number On the Argand diagram:real x y and it is also 2 real

© 2005 Baylor University Slide 7 Complex Number Functions in the TI-89 real

© 2005 Baylor University Slide 8 Polar Form of the Complex Number If then The Polar Form - by substituting is: recall

© 2005 Baylor University Slide 9 Questions?