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Warm-Up: December 13, 2011 Solve for x:

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Complex Numbers Section 2.1

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Imaginary Unit, i

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Imaginary Numbers Multiples of i are imaginary numbers. Square roots of negative numbers are imaginary.

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Complex Numbers Any number that can be written in the form “ a+b i ” is a complex number. This is called the standard form. In “a+bi” both a and b are real numbers a is called the real part b is called the imaginary part A complex number is simplified iff it is written in standard form, “ a+b i ”

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Operations with Complex Numbers Addition: Combine like terms Add the real parts, add the imaginary parts Subtraction: Combine like terms Subtract the real parts, subtract imaginary parts Don’t forget to distribute the negative Multiplication: Use distributive property or FOIL Replace i 2 with -1 Always write final answer in standard form, “ a+b i ”

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Example 1 (like HW #1-8)

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You-Try #1 (like HW #1-8)

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Example 2 (like HW #9-20)

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You-Try #2 (like HW #9-20)

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Complex Conjugates The complex conjugate of “ a+b i ” is “ a-b i ” Switch the sign of the imaginary part The product of a complex number and its complex conjugate is:

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Warm-Up: December 6, 2010

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Warm-Up: December 7, 2010

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Dividing Complex Numbers 1. Multiply the numerator and denominator by the complex conjugate of the denominator 2. FOIL the numerator and simplify 3. Denominator becomes a 2 +b 2 4. Write the result in standard form

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Example 3 (like HW #21-28)

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Warm-Up: December 14, 2011

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Homework Questions?

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You-Try #3 (like HW #21-28)

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Principal Square Root of Negative Numbers Product and quotient properties of square roots do not apply to square roots of negative numbers. Take out the i before multiplying or dividing square roots

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Example 4 (like HW #29-44) Perform the indicated operations and write the result in standard form

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You-Try #4 (like HW #29-44) Perform the indicated operations and write the result in standard form

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Quadratic Formula It works to find complex solutions of quadratic equations, not just real ones.

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Example 5 (like HW #45-50) Solve for x. Express solutions in standard form.

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You-Try #5 (like HW #45-50) Solve for x. Express solutions in standard form.

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Assignment Page 252 #1-49 Every Other Odd

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