MAT 1341 Lecture 2: Lecture#2
15 May 2016
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Document Summary
Usually de ne as a geometric object that has both magnitude and direction. What is the polar representation of the complex number z=-3? z=-3 z=3 you may say z = 3ei0, but that would be wrong, because you the direction is wrong. The correct polar representation is z = 3ei . To see this recall that if z = a + bi, thenr = a2 + b2 and cos( ) = a r . 3 therefore ( = cos 1( 1) = ) and sin( ) = 0 cos( ) = 3: and z = 3cos(pi) + 3sin(0) = ei . : has magnitude and always travel in future. Vectors are geometric objects that are manipulated (add etc) by vector algebra. To understand what we mean: v1 and v2 the addition of v1 + v2 = v = (a, b). |v| 6= |v1| + |v2|, but |v| = p|v1| + |v2|.
