1. Complex Numbers include Real numbers and Imaginary Numbers
Define i = Practice
Complex Numbers include Real numbers and Imaginary Numbers
Powers of i: i1 =
i2 =
i3 =
i4 =
i5 =
i6 =
i7 =
i8 =
What about i12? What about i15?
A short cut to find any power of i: Divide the exponent by 4 and find the remainder
i5 →
i15 →
i12 →
i43 →
Simplify i Simplify i234 1

2. e) Challenge: Simplify
Simplify the following by getting all negatives outside the square root
a) b) c) d)
e) Challenge: Simplify
Operations with Complex Numbers:
Add/subtract complex numbers by combining real and imaginary separately
Multiply complex numbers by FOIL (use i properties to simplify)
Simplify the following:
(3 + 5i) + (8 – i) b) (9 – 3i) – (2 – 8i)
c) -4 – (1 + i) – (5 + 9i) d) 10 – (6 + 7i) + 4i 2

3. Simplify the following (8 – 7i)(3 + 4i) b)
c) d) ( 6 + 2i)(6 – 2i)
(a + bi) and (a – bi) are called complex conjugates (look at b and d above)
What is the difference between the two?
What do you notice when complex conjugates are multiplied?
Find the following for f(x) = 2x2 – 6x + 5
Vertex:
y-intercept
zeros 3