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Complex Numbers and Solving Equations

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Presentation on theme: "Complex Numbers and Solving Equations"โ€” Presentation transcript:

1 Complex Numbers and Solving Equations
Honors Algebra II with Trig. Mr. Agnew

2 Essential Stuff Essential Question Essential Vocabulary
How do you simplify expressions involving complex numbers? Essential Vocabulary Imaginary Number Complex Number Complex Conjugate

3 Imaginary Numbers Not all quadratic equations have real number solutions, so to overcome this problem, mathematicians created an expanded system of numbers using the imaginary unit ๐ข

4 Imaginary Unit, ๐’Š ๐’Š= โˆ’๐Ÿ ๐’Š ๐Ÿ =โˆ’๐Ÿ These properties allow us to simply the square root of a negative number.

5 Complex Numbers A complex number is a number that contains a real and an imaginary part. The standard form: ๐’‚+๐’ƒ๐’Š Real Imaginary

6 Add/Subtract/Multiply
Add and Subtract Combine Like Terms Write in Standard Form Multiply FOIL Replace ๐’Š ๐Ÿ with โˆ’๐Ÿ Combine Like Terms/Standard Form

7 Dividing with Complex Numbers
Divide Multiply the numerator and denominator by the complex conjugate Complex conjugates are two complex numbers of the form: ๐’‚+๐’ƒ๐’Š and ๐’‚โˆ’๐’ƒ๐’Š

8 The product of complex conjugates will always be a real number.

9 Homework Homework 5.5: Complex Numbers


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