Complex Numbers - h1014v2

Imaginary Numbers - h1014v2_79

Complex Numbers - h1014v2_81

Mathematics Volume 2 of 2
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IMAGINARY AND COMPLEX NUMBERS Higher Concepts of Mathematics Complex Numbers Complex numbers are numbers which consist of a real part and an imaginary part. The solution of some quadratic and higher degree equations results in complex numbers. For example, the roots of the quadratic equation, x² - 4x + 13 = 0, are complex numbers. Using the quadratic formula yields two complex numbers as roots. x b b² 4ac 2a x 4 16 52 2 x 4 36 2 x 4 6i 2 x 2 3i The two roots are 2 + 3i and 2 - 3i; they are both complex numbers. 2 is the real part; +3i and - 3i are the imaginary parts. The general form of a complex number is a + bi, in which "a" represents the real part and "bi" represents the imaginary part. Complex numbers are added, subtracted, multiplied, and divided like algebraic binomials. Thus, the sum of the two complex numbers, 7 + 5i and 2 + 3i is 9 + 8i, and 7 + 5i minus 2 + 3i, is 5 + 2i. Similarly, the product of 7 + 5i and 2 + 3i is 14 + 31i +15i². But i² equals -1. Thus, the product is 14 + 31i + 15(-1) which equals -1 + 31i. Example 1: Combine the following complex numbers: (4 + 3i) + (8 - 2i) - (7 + 3i) = Solution: (4 + 3i) + (8 - 2i) - (7 + 3i) = (4 + 8 - 7) + (3 - 2 - 3)i = 5 - 2i MA-05 Page 14 Rev. 0

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