9.3-one - 9.3 The Complex Plane; De Moivre’s Theorem...

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Unformatted text preview: 9.3 The Complex Plane; De Moivre’s Theorem Complex plane Imaginary axis :E'; 3-3-3“. 1. Plot Points in the Complex Plane Let z 2 x + yz' be a complex number. The magnitude or modulus of :. denoted by is defined as the distance from the origin to the point (x. y). That is. Imaginary axis *“_ ~ 2” X “j Z : XMLLj 2meafiflbmflwfihmfixmmflkamgmufimandemm If r 2 0 and 0 s 6 < 277, the complex number z = x + yi may be written in polar form as Z = x + yi = (r (:05 9) + (r sin 9)i = r(c059 + isin 6) (4) Imaginary :Z '2. x + ij x ——_ rcoge mus z=x+yi=r(cosfl+isin6), = : .‘L "L €£EZ$£L r2Q036<2w ‘Zl r JK+W . J a k C “3&7 " ___—————-—-: E a. ’21:— X +L LS - ‘ - *— " mm X:3 %;F&m -. —JU%¢9)4— h’flf#fiflffi*,,_ 3”: JVHIL : \J tzmsza +‘ra—${029' fi_;flr,# 1 \l 52+ ("$133) 9’ __Ffl_f§flfl_fi_flfla ,‘I —. L 2... _" 3-9 ~d9+9$3 —\Jk U%39+%m ) 473? ___ Y : 6 Z. \I r2- ...
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9.3-one - 9.3 The Complex Plane; De Moivre’s Theorem...

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