1. 5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.

2. Imaginary Unit i  i 2 = -1  i = √-1  The imaginary unit i can be used to write the square root of any negative number.

4. The Square Root of a Negative Number

5. Example 1: Solve a Quadratic Equation  7 x 2 = -49  3 x 2 – 5 = -29

6. Checkpoint:  x 2 = -3  x 2 = -20  x 2 - 4 = -12  x 2 = -7  x 2 + 3 = -2  2 x 2 + 7 = -17

7. Complex Numbers  Written in standard form is a number a + bi  a and b are real numbers  a is the real part of the complex number  b is the imaginary part of the complex number

8. Complex Numbers

9. Examples 2 and 3:  (3 + 2i) + (1 – i)  (6 – 2i) – (1 – 2i) Add Complex NumbersSubtract Complex Numbers

10. Checkpoint:  (4 – 2i) + (1 + 3i)  (3 – i) + (2 + 4i)  (4 + 6i) – (2 + 3i)  (-2 + 4i) – (2 + 7i)  (1 – 2i) + (4 + 5i)  (2 – i) – (-1 – 4i)

11. p. 264 – 265 # 16 – 38 even, 59-63, 72, 73 Homework Day 1:

12. Example 4: Multiply Complex Numbers  2i(-1 + 3i)  (6 + 3i)(4 – 3i)

13. Checkpoint:  3i(2 – i)  (1 + 2i)(2 – i)

14. Example 5: Dividing Complex Numbers  3 + 2i 1 – 2i  2 + i 1 - i

16. p. 264 – 265 #40 – 58 even, 64-67, 74 Homework Day 2: