1. Warm Up for 1.1 in Math 2 ANSWER 1. Simplify 3 4 – 5 12 + 3 5 11

2. 1.1 (M2)Writing Complex Numbers

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 pattern to describe the square root of a negative number after they thought all real numbers were identified

4. Complex Numbers (a + bi) Real Numbers (a + 0i) -1½ pi√3 Imaginary Numbers (a + bi, b ≠ 0) 2 + 3i5-5i Pure Imaginary Numbers (0 + bi, b ≠ 0) -4i5i

5. 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

6. Write the complex number in standard form. 1. √-12. √-25 i5i 3. 2 - √-94. 7 - √-27 2 -3i7-3i√3

7. Find real numbers x and y to make the equation true.Find real numbers x and y to make the equation true. -3x + 2yi = 15 – 4i-3x + 2yi = 15 – 4i 11 – 5yi = x + 10i11 – 5yi = x + 10i 22 – 8i = 11x + 4yi22 – 8i = 11x + 4yi