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Unformatted text preview: 1 tan 2 2 a< < . Then a specific value of n in the above expression leads to a single value for the angle. Obviously, for any real number 2 n = . The trigonometric representation facilitates many calculations. For example, powers become very easy, as ( ) k k k ik z x iy z e φ = + = . Inverses and roots are easily calculated as negative or fractional powers. For example, to find the third (cube) roots of 2 1 n i z e π = = one writes 1 3 2 /3 2 2 cos sin 3 3 n i n n z e i = = + . Distinct roots occur for n = : 1/3 1 z = 1 n = : 1/3 1 3 2 2 z i = + , 2 n = : 1/3 1 3 2 2 z i = . (Other values of n produce the same results.)...
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This note was uploaded on 02/08/2012 for the course CHEM 540 taught by Professor Mccall during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Mccall
 pH

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