1. Complex Numbers We haven’t been allowed to take the square root of a negative number, but there is a way: Define the imaginary number For example,

2. Ex. Simplify a) b)

3. A complex number in standard form looks like: a + bi, where a and b are real numbers. In the complex number 5 + 3i, 5 is the real part 3 is the imaginary part  If b = 0, it is a real number

4. Add and subtract by combining like terms Ex. Write as a complex number in standard form.

5. Multiply by foiling  don’t forget i 2 = -1 Ex. Simplify

6. Ex. Write as a complex number in standard form.

7. If a complex number looks like a + bi, its complex conjugate will be a – bi. Ex. Write the complex conjugate of 6 – 5i, then multiply them.  The product of a complex number and its conjugate is always a real number  This can be used to rationalize the denominator

8. Ex. Write as a complex number in standard form.

11. Ex. Evaluate i 13