Complex Number Review How much do you remember? (10.2)

POD Calculate the following. Up to the board.

SAT Prep SAT #1

SAT Prep SAT #2

SAT Prep SAT #3

Review the cycle Remember what happens with successive powers of i?

Review the cycle Remember what happens with successive powers of i?

Review the cycle Remember what happens with successive powers of i? Here’s a way to keep track of the pattern. What would i 23 equal? What would i 101 equal? i -i 1

Connection to radical signs What is the definition of i? Using that, rewrite the following.

Connection to radical signs What is the definition of i? Using that, rewrite the following.

Graphing complex numbers What sort of coordinate system do we use to graph complex numbers? What is on each axis? Plot 7+11i, 5-2i, 3, -9i.

Graphing complex numbers What connection do you see between this axis and our pattern shortcut? i -i 1

Adding and subtracting complex numbers Like adding polynomials, you combine like terms.

Adding and subtracting complex numbers Like adding polynomials, you combine like terms.

Multiplying complex numbers Like multiplying binomials, you FOIL.

Multiplying complex numbers Like multiplying binomials, you FOIL.

Complex conjugates Give the complex conjugates of the following.

Complex conjugates Give the complex conjugates of the following.

Complex conjugates Multiply the complex conjugates. What happens?

Complex conjugates Multiply the complex conjugates. What happens?

Complex conjugates Multiply the complex conjugates. What happens? General rule: So, how would you factor (x 2 + 9)?

Dividing complex numbers Multiplying complex conjugates comes into play here so we can eliminate the complex numbers in the denominator.

Dividing complex numbers Multiplying complex conjugates comes into play here so we can eliminate the complex numbers in the denominator. What are the real and imaginary components?

Make up your own Choose one operation– addition, subtraction, multiplication, or division– make up your own numbers, and solve. Everyone put a problem on the board!