1. 7.7 Complex Numbers

2. Imaginary numbers and Powers of i

3. Square Roots of Negative #’s

4. Complex Numbers a is the real part
Definition: Any number that can be written in the form a+bi
a is the real part
b is the coefficient of the imaginary part

5. Arithmetic Operations
(3+7i) + (2-5i)
= 5+2i
• (3+7i) - (2-5i)
= 1+12i
• (3+7i)(2-5i)
= 6-15i +14i -35i²
= 6-i+35
=41-i

6. Complex Conjugates # conjugate 3+2i 3-2i 1-i 1+i 4i -4i 0+4i 0-4i 5 5
5 5
5+0i 5-0i

7. Dividing complex numbers
• multiply numerator/denominator by conjugate of denominator
• Ex.