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Notes 29 Operations with Complex Numbers Objectives: Perform operations with complex numbers Why learn this? Complex numbers can be used in formulas to create patterns called fractals. 1 Just as you can represent real numbers graphically as points in a coordinate plane, you can represent complex numbers in a special coordinate plane... The complex plane is a set of coordinate axes in which the horizontal axis represents real numbers and the vertical axis represents imaginary numbers. 2 Ex. Graph each complex number. a. b. c. d. 3 Try These: Ex. Graph each complex number. a. b. c. d. 4 Ex. Find each absolute value. a. b. c. 5 Try These: Ex. Find each absolute value. a. b. c. 6 Adding and subtracting complex numbers is similar to adding and subtracting variable expressions.... COLLECT LIKE TERMS!! Ex. Add or subtract. Write the result in the form a + bi. a. b. c. d. 7 To multiply complex numbers... distribute! Ex. Multiply. Write the result in the form a + bi a. b. c. d. 8 Review powers of i... Ex. Simplify. a. b. 9 Try These: Ex. Simplify. a. b. 10 Recall that expressions in simplest form cannot have square roots in the denominator... Ex. Simplify a. b. 11 Try These: Ex. Simplify. a. b. 12