1. Imaginary & Complex Numbers Mini Unit

2. Once upon a time…

3. -In the set of real numbers, negative numbers do not have square roots.
-Imaginary numbers were invented so that negative numbers would have square roots and certain equations would have solutions.
-These numbers were devised using an imaginary unit named i.

4. -The imaginary numbers consist of all numbers bi, where b is a real number and i is the imaginary unit, with the property that i² = -1.
-The first four powers of i establish an important pattern and should be memorized.
Powers of i

5. Powers of i Divide the exponent by 4 No remainder: answer is 1.
remainder of 1: answer is i.
remainder of 2: answer is –1.
remainder of 3:answer is –i.

6. Powers of i
1.) Find i23
2.) Find i2006
3.) Find i37

7. Complex Number System Reals Rationals (fractions, decimals) Integers
Imaginary
i, 2i, -3-7i, etc.
Rationals
(fractions, decimals)
Integers
(…, -1, -2, 0, 1, 2, …)
Irrationals
(no fractions)
pi, e
Whole
(0, 1, 2, …)
Natural
(1, 2, …)

8. a + bi imaginary real Complex Numbers
The complex numbers consist of all sums a + bi, where a and b are real numbers and i is the imaginary unit. The real part is a, and the imaginary part is bi.

9. Add or Subtract
ex.
ex.
ex.

10. Complex Numbers
Find the value of x and y that makes 5𝑥+1+ 3−2𝑦 𝑖=11−13𝑖 true.

11. REMEMBER: i² = -1
Multiply 1) 2)

12. Multiply
ex)

13. Complex numbers are defined as 𝑎+𝑏𝑖, where 𝑎 and 𝑏 are real numbers and 𝑖 is the imaginary unit. Given 2−2𝑖 3+5𝑖 , what is 𝑎+𝑏?

14. Assignment
Pg #18−32 even #36−44 even #66

15. Questions on Assignment
Pg #18−32 even #36−44 even #66

16. Conjugate -The conjugate of a + bi is a – bi

17. Find the conjugate of each number…8) 9)
10)
11)

18. Divide…
12)

19. You try…
13)