1. Complex Numbers

2.  Numbers that are not real are called Imaginary. They use the letter i.  i = √-1 or i 2 = -1  Simplify each: √-81 √-10 √-32 √-810

3.  A Complex Number is a number that has both a Real and an Imaginary component.  Written in the form a + bi  a is the REAL number  bi is the IMAGINARY number  To add, subtract, or multiply complex numbers, just treat them like binomials.  Don’t forget… i 2 = -1

4.  1. (6 + 4i) + (-2 – 2i)  2.(-14 + 2i) – (6 + i) + (19 + 10i)  3.(4i)(-7i)  4.(6 – 3i)(7 + 8i)  5.(5 – 3i) 2

5.  Use the CONJUGATE  The conjugate of (a + bi) is (a – bi)  The conjugate of (bi) is (-bi)  Multiply both the numerator and the denominator by the complex conjugate and simplify… write the answer as a + bi  Remember: i 2 = -1

6. 1. 6 2. 3 + i 7i 3i 3. 3 + i 4. 5 – 6i 2 – i 2 – 9i