Section 1.4 Complex Numbers

Observe what happens when we multiply a complex

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Unformatted text preview: mbers Complex Conjugates The complex conjugate of a + bi is the complex number a − bi . Observe what happens when we multiply a complex number by its conjugate: (a + bi )(a − bi ) = a2 − abi + abi − bi 2 = a2 + b 2 . In particular, the product of complex conjugates is a real number: (a + bi )(a − bi ) = a2 + b 2 Example 1 Multiply 1 + i and its conjugate. 2 Multiply 4 − 3i and its conjugate. Outline Imaginary Numbers Complex Numbers The Arithmetic of the Complex Numbers Dividing Complex Numbers When we divide a + bi by c + di , we get a number of the form: a + bi . c + di This is a complex number! We put it in standard form by multiplying numerator and denominator by c − di (the complex conjugate of the denominator) and simplifying. Example 1 Divide 2 + i by 1 − 3i , then put the result in standard form. 2 Divide −4 + 8i by 2 − 4i , then put the result in standard form....
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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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