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What is the imaginary unit i ? What is a complex number? Identify the imaginary and real parts of a complex number. Practice - see textbook p.103 #7 – 42 1.3 Complex Numbers http://www.youtube.com/watch?v=NeTRNpBI17I

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Add and Subtract Complex Numbers Practice - see textbook p.103 #43 - 50 Add the real parts and the imaginary parts, just like combining like terms. Be sure to distribute the negative sign when subtracting! http://www.youtube.com/watch?v=eyy_SR1JfyQ&feature=youtu.be

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http://www.youtube.com/watch?v=O9xQaIi0NX0 Multiplying easy complex numbers * Remember i 2 = -1

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Multiplying complex numbers Practice - see textbook p.103 #51- 68 http://www.youtube.com/watch?v=Fmr3o2zkwLM&feature=youtu.be

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Complex numbers and their conjugate The conjugate of a complex number is simply the same complex number with the sign changed on the imaginary part. When you multiply a complex number by the conjugate, the product simplifies to a real number with no imaginary part. Complex conjugates are needed for division of complex numbers. http://www.youtube.com/watch?v=VbOzEkvMb_A&feature=youtu.be

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Dividing complex numbers To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator and simplify. Practice - see textbook p.103 #69 – 80 http://www.youtube.com/watch?v=XBJjbJAwM1c

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Practice - see textbook p.103 #85 - 96 Simplifying powers of i http://www.youtube.com/watch?v=sfP6SmEYHRw

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What you should know: Add and Subtract complex numbers Imaginary part Real part Complex number Imaginary unit Divide complex numbers Multiply complex numbers Simplify radicals with negative radicands Standard form Quotient Complex conjugate Numerator Denominator Product Powers of i 1.3 Complex Numbers

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Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

Section 8.7 Complex Numbers. Overview In previous sections, it was not possible to find the square root of a negative number using real numbers: is not.

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