1. Complex numbers
Math 3 Honors

2. solve 4 81 16
144
−4 *
−16 * ±2 ±9 ±4
±12
±2𝑖
±4𝑖

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4. 𝑖= −1
So, what else do you know?
𝑖 2 =−1
𝑖 3 =−𝑖
𝑖 4 =1

5. simplify (HINT: Divide by 4 and use remainder to simplify) 𝑖 23 𝑖 2006
𝑖 37
𝑖 828 −𝑖 −1 𝑖 1

6. Complex numbers have real and imaginary part
𝑎+𝑏𝑖

7. Add and subtract 7𝑖+9𝑖 −5+6𝑖 +(2−11𝑖) 2+3𝑖 − 4+2𝑖 −3+4𝑖 − 1+3𝑖
3−4𝑖 + 2−7𝑖 −(5−12𝑖)
16𝑖
−3−5𝑖
−2+𝑖
−4+𝑖 𝑖

8. multiply (2+5𝑖)(7+2𝑖) (7−4𝑖)(3+4𝑖) (2+3𝑖)(14+8𝑖) (5−4𝑖)(−11+15𝑖) 4+39𝑖
37+16𝑖
4+58𝑖
5+119𝑖

9. To divide: Multiply both parts by the conjugate of the bottom
**Conjugate of (a+bi) = (a-bi)

10. Why must we do that?
We can’t have 𝑖 in the denominator and the conjugate will cancel out the middle term for us!

11. Divide −3+𝑖 5−2𝑖 (60+90𝑖)÷(14+8𝑖) (−33−56𝑖) (5−12𝑖)
(−63+23𝑖)÷(−11+15𝑖)
−17−𝑖 29
6+3𝑖
3−4𝑖
3+2𝑖