Chap 1 The Number System

Express each of the following numbers in the form x y

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Unformatted text preview: bers of the form a + bi, where a, b ∈ R and i2 = −1. Such numbers can be represented on the xy -plane by points of the form (a, b). a) Consider the complex number 3 + 4i, represented on the xy -plane by the point (3, 4). Draw a picture of the xy -plane, clearly indicating the origin (0, 0) and the point (3, 4). b) Draw a line segment joining (0, 0) and (3, 4). What is the length of this line segment? c) We now multiply the complex number 3 + 4i by the complex number i to obtain the product i(3 + 4i). Which point on the xy -plane represents the number i(3 + 4i)? Indicate this point on the xy -plane. d) Draw a line segment joining (0, 0) and the point in part (c). What is the length of this line segment? What is the angle between this line segment and the line segment in part (b)? e) Which point on the xy -plane represents the number 2i(3+4i)? Indicate this point on the xy -plane. Draw a line segment joining (0, 0) and this point. What is the length of this line segment? What is the angle between this line segment and the line segm...
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