Warm-Up: December 13, 2011  Solve for x:

Complex Numbers Section 2.1

Imaginary Unit, i

Imaginary Numbers  Multiples of i are imaginary numbers.  Square roots of negative numbers are imaginary.

Complex Numbers  Any number that can be written in the form “ a+b i ” is a complex number. This is called the standard form.  In “a+bi” both a and b are real numbers  a is called the real part  b is called the imaginary part  A complex number is simplified iff it is written in standard form, “ a+b i ”

Operations with Complex Numbers  Addition: Combine like terms  Add the real parts, add the imaginary parts  Subtraction: Combine like terms  Subtract the real parts, subtract imaginary parts  Don’t forget to distribute the negative  Multiplication: Use distributive property or FOIL  Replace i 2 with -1  Always write final answer in standard form, “ a+b i ”

Example 1 (like HW #1-8)

You-Try #1 (like HW #1-8)

Example 2 (like HW #9-20)

You-Try #2 (like HW #9-20)

Complex Conjugates  The complex conjugate of “ a+b i ” is “ a-b i ”  Switch the sign of the imaginary part  The product of a complex number and its complex conjugate is:

Warm-Up: December 6, 2010

Warm-Up: December 7, 2010

Dividing Complex Numbers 1. Multiply the numerator and denominator by the complex conjugate of the denominator 2. FOIL the numerator and simplify 3. Denominator becomes a 2 +b 2 4. Write the result in standard form

Example 3 (like HW #21-28)

Warm-Up: December 14, 2011

Homework Questions?

You-Try #3 (like HW #21-28)

Principal Square Root of Negative Numbers  Product and quotient properties of square roots do not apply to square roots of negative numbers.  Take out the i before multiplying or dividing square roots

Example 4 (like HW #29-44)  Perform the indicated operations and write the result in standard form

You-Try #4 (like HW #29-44)  Perform the indicated operations and write the result in standard form

Quadratic Formula  It works to find complex solutions of quadratic equations, not just real ones.

Example 5 (like HW #45-50)  Solve for x. Express solutions in standard form.

You-Try #5 (like HW #45-50)  Solve for x. Express solutions in standard form.

Assignment  Page 252 #1-49 Every Other Odd