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# Complex Numbers

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## Chloe Weiers

on 29 September 2012

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#### Transcript of Complex Numbers

2.4 Complex Numbers x²+1=0 The Imaginary Unit i A complex conjugate is simply the original complex number (a+bi) in the form (a-bi). Complex Conjugates Addition and Subtraction Operations with Complex Numbers Complex Solutions of Quadratic Equations pg 133 (7-10, 15-90 [mod 5]) Suggested Homework Example 1 A square root of a negative creates an imaginary number
So i=√-1 i²=-1 √-9 -5=0
3√-1-5=0
3i-5=0 You cannot combine imaginary and real numbers. Multiply the complex number by its complex conjugate.
6-4i Division Using Complex Conjugates To divide two complex numbers, multiply both complex numbers by the bottom number's complex conjugate. 8-7i (1+2i)
1-2i (1+2i) 1) 2) Use the distributive property on both top and bottom. 8+16i-7i-14i²
1-2i+2i-4i² Remember that i²=-1, so you substitute in -1 for every i². 3) 8+9i-14(-1)
1-4(-1) 4) This becomes +14. This becomes +4. 22+9i