2. Square Root of a Negative Number You’re not allowed to have a negative number under the radical sign. Let me show you how it works The Imaginary Unit The Imaginary Unit is denoted as: i The Imaginary Unit is used to find the square root of negative numbers. These are all examples of Pure Imaginary Numbers. A Pure Imaginary Number is the product of any real number and i.i.

3. Complex Numbers The sum of a real number and a pure imaginary number is called a Complex Number. The standard form of a Complex Number is Examples: How is that a complex number. There’s no i. I never imagined that imaginary numbers would be so easy.

4. Properties of Complex Numbers Adding, subtracting, multiplying, and dividing complex numbers works the same way as with regular binomials with real numbers and variables. Let’s take a look at some examples.

5. Operations with Complex Numbers I’d like to push the easy button now.

6. Powers of i Hey, it’s Sam Ting again. Every 4 th power repeats. So you only need to know the first 4 powers of i. When the power of i is greater than 4, divide by 4 and use the remainder to find the simplified value.

7. Simplifying Powers of i

8. Complex Conjugates Complex Conjugates are two complex numbers that are the same with the exception of the sign in the middle. The product of a pair of Complex Conjugates is always a positive real number. This should be pretty easy. We did this conjugate stuff before with radicals

9. Complex Conjugates Complex Conjugates are two complex numbers that are the same with the exception of the sign in the middle. The product of a pair of Complex Conjugates is always a positive real number. Let’s use foil first. Hey, I can use a stupid human trick for this too! This should be pretty easy. We did this conjugate stuff before with radicals.

10. Multiplying Complex Conjugates Multiply each number by its complex conjugate.

11. Dividing Complex Numbers Complex Conjugates are used to divide by a complex number the same way that regular conjugates are used to rationalize a denominator with a radical in it.

12. Dividing Complex Numbers Complex Conjugates are used to divide by a complex number the same way that regular conjugates are used to rationalize a denominator with a radical in it. Can I do this on my calculator? Holy schnikies, it works! Asi De Facil

13. Complex Numbers Homework Amsco Online Textbook Chapter 5: Page 216 27 – 37 Odd #’s Only 47 – 53 Odd #’s Only

14. Multiplicative Inverse of a Complex Number Write the multiplicative inverse, in standard a + bi form, of The multiplicative inverse of a complex number is its reciprocal. Write the multiplicative inverse, in standard a + bi form, of This complex number stuff is not that complex.

15. Complex Numbers Homework Amsco Online Textbook Chapter 5: Page 216 27 – 53 Odd #’s Only

16. Graphing Complex Numbers When a complex number is graphed in the Complex Plane, the horizontal axis is the Real axis and the vertical axis is the Imaginary axis. Real Imaginary Graph the following complex numbers. a) 2 + 3i b) 2 - 4i c) -4 + 2i d) -2 - 3i 4i 3i 2i i -i -2i -3i -4 i 2 + 3i 2 - 4i -4 + 2i -2 - 3i So easy, even a caveman can do it.

17. More Graphing Complex Numbers When a complex number is graphed in the Complex Plane, the horizontal axis is the Real axis and the vertical axis is the Imaginary axis. Let Z 1 = 2 + 4i and let Z 2 = -3 - 2i a)Graph both on the same axes. b)Determine Z 1 + Z 2. 2 + 4i -3 - 2i -1 + 2i Real Imaginary That was easy