Section 1.4 Complex Numbers

Example add or subtract 1 7 72 8 50 2 3 6 5i

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Unformatted text preview: − (c + di ) = (a − c ) + (b − d )i . Example Add or Subtract. √ √ 1 (−7 − −72) + (8 + −50). 2 3 (6 − 5i ) − (4 + 3i ). 5 1 −6 − i + 4 + i 8 2 Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers Multiplying Complex Numbers We multiply complex numbers using the distributive law: (a + bi )(c + di ) = a(c + di ) + bi (c + di ) = ac + adi + bci + bdi 2 = (ac − bd ) + (ad + bc )i . Example Multiply: 1 3(2 − 3i ). 2 (6i )(−3 + 7i ). 3 (2 − 3i )(−5 + i ). 4 Check that x = −7i is a solution of x 2 + 49. 5 Check that x = −1 + 2i is a solution of (x + 1)2 = −4. Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers Powers of i Observe the following pattern: i 0 = 1 i 1 = i i 2 = −1 i 3 = −i i 4 = 1 i 5 = i i 6 = −1 i 7 = −i i 8 = 1 i 9 = i i 10 = −1 i 11 = −i . . . . . . . . . . . . Notice that the pattern repeats every four power increments. We deduce that i 4m+k = i k . Example 1 What is i 39 ? 2 What is i 74 ? Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Nu...
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This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.

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