1. Warm Up for 1.1 in Math 2 2.3x 2 + 8 = 23 ANSWER 5, – 5 1. Simplify 3 4 – 5 Solve the equation. 12 + 3 5 11 3.2(x + 7) 2 = 16 Solve the equation. ANSWER –7 + 2 2, –7 – 2 2 4. Three times the square of a number is 15. What is the number? – 5, 5 ANSWER

2. 1.1 Writing Complex Numbers Purple Math 2 Book

3. Solve x 2 + 4 = 0 x 2 = -4 x = √(-4) In the real number system, there isn’t a number we can square to get -4. Imaginary numbers: Don’t think of them as “not real” Mathematicians chose this term for the square root of a negative number after they thought all real numbers were identified-(thought no real life application)

4. Imaginary Numbers

5. The square root of negative numbers Examples:

6. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:

7. Complex Numbers A complex number has a real part & an imaginary part.A complex number has a real part & an imaginary part. Standard form is:Standard form is: Real part Imaginary part Example: 5+4i

8. i Anytime you have √-1, you replace it with iAnytime you have √-1, you replace it with i √-16√-16 √16 * √-1√16 * √-1 4 * i4 * i 4i4i

9. How do we write the square root of a negative number? √-1 is called i or an imaginary unit—it is a way to describe the square root of a negative number√-1 is called i or an imaginary unit—it is a way to describe the square root of a negative number (√-1 ) 2(√-1 ) 2 √-1 * √-1√-1 * √-1 Therefore, i 2 = -1.Therefore, i 2 = -1. i = √-1 i 2 = -1i = √-1 i 2 = -1 i 3 = (√-1 ) 3 = -ii 3 = (√-1 ) 3 = -i i 4 = (√-1 ) 4 = -1*-1 = 1i 4 = (√-1 ) 4 = -1*-1 = 1

10. Write the complex number in standard form. 1. √-12. √-25 i5i 3. √-84. √-32 2i √2 4i √2 2i √2 4i √2

11. Complex Numbers (a + bi) real (a) + imaginary (bi) Real Numbers Just a (a + 0i) -1½ pi√3 Imaginary Numbers (a + bi, b ≠ 0) 2 + 3i5-5i Pure Imaginary Numbers (0 + bi, b ≠ 0, no a) -4i5i

12. Write the complex number in standard form. 5. 2 - √-96. 7 - √-27 2 -3i7-3i√3

13. With a partner, do p. 3 in M2 #’s 1-10